Feynman path integrals in quantum mechanics and statistical physics:
"This book provides an ideal introduction to the use of Feynman Path Integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in...
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| Format: | Buch |
| Sprache: | English |
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Boca Raton ; London ; New York
CRC Press
2021
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| Ausgabe: | First edition |
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| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This book provides an ideal introduction to the use of Feynman Path Integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations"-- |
| Beschreibung: | Literaturverzeichnis: Seite 391-393 |
| Beschreibung: | xiv, 400 Seiten Illustrationen, Diagramme |
| ISBN: | 9780367697853 9780367702991 |
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| 100 | 1 | |a Fai, Lukong Cornelius |d 1961- |e Verfasser |0 (DE-588)1191949486 |4 aut | |
| 245 | 1 | 0 | |a Feynman path integrals in quantum mechanics and statistical physics |c Professor Lukong Cornelius Fai |
| 250 | |a First edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2021 | |
| 300 | |a xiv, 400 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis: Seite 391-393 | ||
| 520 | 3 | |a "This book provides an ideal introduction to the use of Feynman Path Integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations"-- | |
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| 653 | 0 | |a Feynman integrals | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-003-14555-4 |
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Datensatz im Suchindex
| _version_ | 1804182553616187392 |
|---|---|
| adam_text | Contents 1 Path Integral Formalism Intuitive Approach 1.1 2 3 Probability Amplitude............................................................................................................ 1 1.1.1 Double Slit Experiment.................................................................................................1 1.1.2 Physical State................................................................................................................ 2 1.1.3 Probability Amplitude.................................................................................................. 2 1.1.4 Revisit Double Slit Experiment.................................................................................... 2 1.1.5 Distinguishability..........................................................................................................3 1.1.6 Superposition Principle................................................................................................ 3 1.1.7 Revisit the Double Slit Experiment/Superposition Principle..................................... 4 1.1.8 Orthogonality............................................................................................................... 5 1.1.9 Orthonormality.............................................................................................................6 1.1.10 Change of Basis.............................................................................................................7 1.1.11 Geometrical Interpretation of State Vector................................................................. 8 1.1.12
Coordinate Transformation..........................................................................................9 1.1.13 Projection Operator.................................................................................................... 10 1.1.14 Continuous Spectrum................................................................................................ 11 Matrix Representation of Linear Operators 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 13 Matrix Element.......................................................................................................................... 13 Linear Self-Adjoint (Hermitian Conjugate) Operators............................................................13 Product of Hermitian Operators...............................................................................................15 Continuous Spectrum................................................................................................................16 Schturm-Liouville Problem: Eigenstates and Eigenvalues.......................................................17 Revisit Linear Self-Adjoint (Hermitian) Operators................................................................. 20 Unitary Transformation............................................................................................................21 Mean (Expectation) Value and Matrix Density.......................................................................22 Degeneracy................................................................................................................................
23 Density Operator....................................................................................................................... 24 Commutativity of Operators.................................................................................................... 25 Operators in Phase Space 3.1 3.2 3.3 3.4 3.5 1 29 Introduction...............................................................................................................................29 Configuration Space.................................................................................................................. 30 Position and Wave Function..................................................................................................... 31 Momentum Space..................................................................................................................... 32 Classical Action......................................................................................................................... 33
Contents VI 4 Transition Amplitude 35 4.1 Path Integration in Phase Space.................................................................................................36 4.1.1 From the Schrödinger Equation to Path Integration.................................................36 4.1.2 Trotter Product Formula..............................................................................................39 4.2 Transition Amplitude................................................................................................................. 41 4.2.1 Hamiltonian Formulation of Path Integration........................................................... 41 4.2.2 Path Integral Subtleties.................................................................................................43 4.2.2.1 Mid-point Rule.............................................................................................43 4.2.3 Lagrangian Formulation of Path Integration............................................................. 44 4.2.3.1 Complex Gaussian Integral....................................................................... 44 4.2.4 Transition Amplitude.................................................................................................. 46 4.2.5 Law for Consecutive Events......................................................................................... 51 4.2.6 Semigroup Property of the Transition Amplitude......................................................51 5 Stationary and Quasi-Classical Approximations 53 5.1 Stationary Phase Method / Fourier
Integral..............................................................................53 5.2 Contribution from Non-Degenerate Stationary Points........................................................... 56 5.2.1 Unique Stationary Point...............................................................................................58 5.3 Quasi-Classical Approximation/Fluctuating Path....................................................................60 5.3.1 Free Particle Classical Action and Transition Amplitude..........................................60 5.3.1.1 Free Particle Classical Action...................................................................... 61 5.3.1.2 Free Particle Transition Amplitude............................................................ 62 5.3.1.3 From Path Integrals to Quantum Mechanics............................................65 5.4 Free and Driven Harmonic Oscillator Classical Action and Transition Amplitude............. 67 5.4.1 Free Oscillator Classical Action................ 67 5.4.2 Driven or Forced Harmonic Oscillator Classical Action...........................................69 5.5 Free and Driven Harmonic Oscillator Transition Amplitude..................................................71 5.6 Fluctuation Contribution to Transition Amplitude..................................................................72 5.6.1 Maslov Correction....................................................................................................... 74 6 Generalized Feynman Path Integration 6.1 6.2 6.3 6.4 Coordinate
Representation........................................................................................................ 77 Free Particle Transition Amplitude............................................................................................79 Gaussian Functional Feynman Path Integrals.......................................................................... 81 Charged Particle in a Magnetic Field........................................................................................ 87 7 From Path Integration to the Schrödinger Equation 7.1 7.2 7.3 7.4 7.5 8.2 8.3 91 Wave Function............................................................................................................................. 91 Schrödinger Equation.................................................................................................................92 The Schrödinger Equation’s Green’s Function.......................................................................... 94 Transition Amplitude for a Time-Independent Hamiltonian................................................. 95 Retarded Green Function........................................................................................................... 97 8 Quasi-Classical Approximation 8.1 77 101 Wentzel-Kramer-Brillouin (WKB) Method............................................................................101 8.1.1 Condition of Applicability of the Quasi- Classical Approximation........................ 104 8.1.2 Bounded Quasi-Classical Motion............................................................................. 106
8.1.3 Quasi-Classical Quantization.................................................................................... 109 8.1.4 Path Integral Link...................................................................................................... Ill Potential Well.............................................................................................................................112 Potential Barrier........................................................................................................................114
Contents 8.4 8.5 8.6 8.7 vii Quasi-Classical Derivation of the Propagator........................................................................116 Reflection and Tunneling via a Barrier.................................................................................. 117 Transparency of the Quasi-Classical Barrier..........................................................................119 Homogenous Field.................................................................................................................. 121 8.7.1 Motion in a Central Symmetric Field...................................................................... 125 8.7.1.1 Polar Equation..........................................................................................125 8.7.1.2 Radial Equation for a Spherically Symmetric Potential in Three Dimensions.............................................................................................. 129 8.7.2 Motion in a Coulombic Field................................................................................... 130 8.7.2.1 Hydrogen Atom........................................................................................130 9 Free Particle and Harmonic Oscillator 9.1 9.2 9.3 135 Eigenfhnction and Eigenvalue................................................................................................ 135 9.1.1 Free Particle.............................................................................................................. 135 9.1.2 Transition Amplitude for a Particle in a Homogenous Field................................. 137
Harmonic Oscillator............................................................................................................... 138 Transition Amplitude Hermiticity..........................................................................................143 10 Matrix Element of a Physical Operator via Functional Integral 145 10.1 Matrix Representation of the Transition Amplitude of a Forced Harmonic Oscillator......147 10.1.1 Charged Particle Interaction with Phonons............................................................ 150 11 Path Integral Perturbation Theory 153 11.1 Time-Dependent Perturbation............................................................................................... 160 11.2 Transition Probability.............................................................................................................163 11.3 Time-Energy Uncertainty Relation....................................................................................... 164 11.4 Density of Final State.............................................................................................................. 166 11.4.1 Transition Rate..........................................................................................................166 11.5 Continuous Spectrum due to a Constant Perturbation........................................................168 11.6 Harmonic Perturbation...........................................................................................................169 12 Transition Matrix Element 173 13 Functional Derivative 179 13.1 Functional Derivative of
the Action Functional.................................................................... 181 13.2 Functional Derivative and Matrix Element............................................................................183 14 Quantum Statistical Mechanics Functional Integral Approach 191 14.1 Introduction.............................................................................................................................191 14.2 Density Matrix.........................................................................................................................191 14.2.1 Partition Function..................................................................................................... 191 14.3 Expectation Value of a Physical Observable.......................................................................... 192 14.4 Density Matrix.........................................................................................................................192 14.5 Density Matrix in the Energy Representation........................................................................194 15 Partition Function and Density Matrix Path Integral Representation 199 15.1 Density Matrix Path Integral Representation.........................................................................199 15.1.1 Density Matrix Operator Average Value in Phase Space........................................ 199 15.1.1.1 Generalized Gaussian Functional Path Integral in Phase Space...........201 15.1.2 Density Matrix via Transition Amplitude................................................................202
15.2 Partition Function in the Path Integral Representation........................................................ 205 15.3 Particle Interaction with a Driven or Forced Harmonic Oscillator: Partition Function....209
Contents viii 15.4 Free Particle Density Matrix and Partition Function............................................................ 121 15.5 Quantum Harmonic Oscillator Density Matrix and Partition Function............................. 214 16 Quasi-Classical Approximation in Quantum Statistical Mechanics 219 16.1 Centroid Effective Potential..................................................................................................... 220 16.2 Expectation Value......................................................................................................................225 17 Feynman Variational Method 18 Polaron Theory 237 18.1 Introduction.............................................................................................................................. 237 18.2 Potaron Energy and Effective Mass..........................................................................................239 18.3 Functional Influence Phase...................................................................................................... 241 18.3.1 Polaron Model Lagrangian........................................................................................243 18.3.2 Polaron Partition Function........................................................................................243 18.4 Influence Phase via Feynman Functional Integral in The Density Matrix Representation.......................................................................................................................... 246 18.4.1 Expectation Value of a Physical
Quantity.................................................................246 18.4.1.1 Density Matrix...........................................................................................246 18.5 Full System Polaron Partition Function in a 3D Structure................................................... 255 18.6 Model System Polaron Partition Function in a 3D Structure...............................................256 18.7 Feynman Inequality and Generating Functional....................................................................257 18.8 Polaron Characteristics in a 3D Structure.............................................................................. 259 18.8.1 Polaron Asymptotic Characteristics......................................................................... 264 18.9 Polaron Characteristics in a Quasi-ID Quantum Wire......................................................... 265 18.9.1 Hamiltonian of the Electron in a Quasi ID Quantum Wire...................................265 18.9.1.1 Lagrangian of the Electron in a Quasi-ID Quantum Wire.................. 266 18.9.1.2 Partition Function of the Electron in a Quasi-ID Quantum Wire......267 18.10 Polaron Generating Function.................................................................................................. 269 18.11 Polaron Asymptotic Characteristics........................................................................................270 18.12 Strong Coupling Regime Polaron Characteristics..................................................................273 18.13 Bipolaron Characteristics in
a Quasi-ID Quantum Wire..................................................... 276 18.13.1 Introduction..................................................................... 276 18.13.2 Bipolaron Diagrammatic Representation.................................................................278 18.13.3 Bipolaron Lagrangian................................................................................................ 278 18.13.4 Bipolaron Equation of Motion.................................................................................280 18.13.5 Transformation into Normal Coordinates................................................................282 18.13.5.1 Diagonalization of the Lagrangian.......................................................... 282 18.13.6 Bipolaron Partition Function................................................................................... 283 18.13.7 Bipolaron Generating Function................................................................................285 18.13.8 Bipolaron Asymptotic Characteristics..................................................................... 286 18.14 Polaron Characteristics in a Quasi-OD Spherical Quantum Dot......................................... 289 18.14.1 Introduction................................................................................................................289 18.14.2 Polaron Lagrangian.................................................................................................... 290 18.14.3 Normal
Modes............................................................................................................290 18.14.4 Lagrangian Diagonalization..................................................................................... 291 18.14.4.1 Transformation to Normal Coordinates................................................. 291 18.14.5 Polaron Partition Function....................................................................................... 292 18.14.6 Generating Function..................................................................................................293 18.15 Bipolaron Characteristics in a Quasi-OD Spherical Quantum Dot......................................295 18.15.1 Introduction................................................................................................................295 18.15.2 Model Lagrangian.................................................................................................... 296 229
Contents ix 18.15.3 Model Lagrangian....................................................................................................296 18.15.3.1 Equation of Motion and Normal Modes...............................................296 18.15.4 Diagonalization of the Lagrangian.........................................................................297 18.15.5 Partition Function...................................................................................................299 18.15.6 Full System Influence Phase................................................................................... 300 18.16 Bipolaran Energy...................................................................................................................300 18.16.1 Generating Function............................................................................................... 300 18.16.2 Bipolaran Characteristics........................................................................................301 18.17 Polaran Characteristics in a Cylindrical Quantum Dot.......................................................304 18.17.1 System Hamiltonian............................................................................................... 304 18.17.2 Transformation to Normal Coordinates................................................................ 305 18.17.2.1 Lagrangian Diagonalization..................................................................305 18.17.3 Polaran Energy/Partition Function........................................................................306 18.17.4 Polaran
Generating Function................................................................................. 307 18.17.5 Polaran Energy........................................................................................................308 18.18 Bipolaran Characteristics in a Cylindrical Quantum Dot................................................... 310 18.18.1 System Hamiltonian............................................................................................... 310 18.18.1.1 Model System Action Functional..........................................................310 18.18.1.2 Equation of Motion / Normal Modes................................................... 311 18.18.1.3 Lagrangian Diagonalization.................................................................. 312 18.18.1.4 Bipolaran Partition Function................................................................. 312 18.18.1.5 Bipolaran Generating Function............................................................. 313 18.18.1.6 В ipolaron Energy....................................................................................313 18.19 Polaran Characteristics in a Quasi-0D Cylindrical Quantum Dot with Asymmetrical Parabolic Potential.........................................................................................315 18.20 Polaran Energy......................................................................................................................316 18.21 Bipolaran Characteristics in a Quasi-0D Cylindrical Quantum Dot with Asymmetrical Parabolic
Potential.........................................................................................320 18.22 Polaran in a Magnetic Field................................................................................................324 19 Multiphoton Absorption by Polarons in a Spherical Quantum Dot 337 19.1 Theory of Multiphoton Absorption by Polarons..................................................................337 19.2 Basic Approximations............................................................................................................338 19.3 Absorption Coefficient..........................................................................................................339 20 Polaronic Kinetics in a Spherical Quantum Dot 351 Kinetic Theory of Gases 365 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 Distribution Function............................................................................................................365 Principle of Detailed Equilibrium......................................................................................... 365 Transport Phenomenon and Boltzmann-Lorentz Kinetic Equation................................... 369 Transport Relaxation Time................................................................................................... 373 Boltzmann H-Theorem......................................................................................................... 375 Thermal Conductivity...........................................................................................................378
Diffusion.................................................................................................................................380 Electron-Phonon System Equation of Motion.....................................................................386 References........................................................................................................................................... 391 Index............. .........................................................................................................................................395
|
| adam_txt |
Contents 1 Path Integral Formalism Intuitive Approach 1.1 2 3 Probability Amplitude. 1 1.1.1 Double Slit Experiment.1 1.1.2 Physical State. 2 1.1.3 Probability Amplitude. 2 1.1.4 Revisit Double Slit Experiment. 2 1.1.5 Distinguishability.3 1.1.6 Superposition Principle. 3 1.1.7 Revisit the Double Slit Experiment/Superposition Principle. 4 1.1.8 Orthogonality. 5 1.1.9 Orthonormality.6 1.1.10 Change of Basis.7 1.1.11 Geometrical Interpretation of State Vector. 8 1.1.12
Coordinate Transformation.9 1.1.13 Projection Operator. 10 1.1.14 Continuous Spectrum. 11 Matrix Representation of Linear Operators 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 13 Matrix Element. 13 Linear Self-Adjoint (Hermitian Conjugate) Operators.13 Product of Hermitian Operators.15 Continuous Spectrum.16 Schturm-Liouville Problem: Eigenstates and Eigenvalues.17 Revisit Linear Self-Adjoint (Hermitian) Operators. 20 Unitary Transformation.21 Mean (Expectation) Value and Matrix Density.22 Degeneracy.
23 Density Operator. 24 Commutativity of Operators. 25 Operators in Phase Space 3.1 3.2 3.3 3.4 3.5 1 29 Introduction.29 Configuration Space. 30 Position and Wave Function. 31 Momentum Space. 32 Classical Action. 33
Contents VI 4 Transition Amplitude 35 4.1 Path Integration in Phase Space.36 4.1.1 From the Schrödinger Equation to Path Integration.36 4.1.2 Trotter Product Formula.39 4.2 Transition Amplitude. 41 4.2.1 Hamiltonian Formulation of Path Integration. 41 4.2.2 Path Integral Subtleties.43 4.2.2.1 Mid-point Rule.43 4.2.3 Lagrangian Formulation of Path Integration. 44 4.2.3.1 Complex Gaussian Integral. 44 4.2.4 Transition Amplitude. 46 4.2.5 Law for Consecutive Events. 51 4.2.6 Semigroup Property of the Transition Amplitude.51 5 Stationary and Quasi-Classical Approximations 53 5.1 Stationary Phase Method / Fourier
Integral.53 5.2 Contribution from Non-Degenerate Stationary Points. 56 5.2.1 Unique Stationary Point.58 5.3 Quasi-Classical Approximation/Fluctuating Path.60 5.3.1 Free Particle Classical Action and Transition Amplitude.60 5.3.1.1 Free Particle Classical Action. 61 5.3.1.2 Free Particle Transition Amplitude. 62 5.3.1.3 From Path Integrals to Quantum Mechanics.65 5.4 Free and Driven Harmonic Oscillator Classical Action and Transition Amplitude. 67 5.4.1 Free Oscillator Classical Action. 67 5.4.2 Driven or Forced Harmonic Oscillator Classical Action.69 5.5 Free and Driven Harmonic Oscillator Transition Amplitude.71 5.6 Fluctuation Contribution to Transition Amplitude.72 5.6.1 Maslov Correction. 74 6 Generalized Feynman Path Integration 6.1 6.2 6.3 6.4 Coordinate
Representation. 77 Free Particle Transition Amplitude.79 Gaussian Functional Feynman Path Integrals. 81 Charged Particle in a Magnetic Field. 87 7 From Path Integration to the Schrödinger Equation 7.1 7.2 7.3 7.4 7.5 8.2 8.3 91 Wave Function. 91 Schrödinger Equation.92 The Schrödinger Equation’s Green’s Function. 94 Transition Amplitude for a Time-Independent Hamiltonian. 95 Retarded Green Function. 97 8 Quasi-Classical Approximation 8.1 77 101 Wentzel-Kramer-Brillouin (WKB) Method.101 8.1.1 Condition of Applicability of the Quasi- Classical Approximation. 104 8.1.2 Bounded Quasi-Classical Motion. 106
8.1.3 Quasi-Classical Quantization. 109 8.1.4 Path Integral Link. Ill Potential Well.112 Potential Barrier.114
Contents 8.4 8.5 8.6 8.7 vii Quasi-Classical Derivation of the Propagator.116 Reflection and Tunneling via a Barrier. 117 Transparency of the Quasi-Classical Barrier.119 Homogenous Field. 121 8.7.1 Motion in a Central Symmetric Field. 125 8.7.1.1 Polar Equation.125 8.7.1.2 Radial Equation for a Spherically Symmetric Potential in Three Dimensions. 129 8.7.2 Motion in a Coulombic Field. 130 8.7.2.1 Hydrogen Atom.130 9 Free Particle and Harmonic Oscillator 9.1 9.2 9.3 135 Eigenfhnction and Eigenvalue. 135 9.1.1 Free Particle. 135 9.1.2 Transition Amplitude for a Particle in a Homogenous Field. 137
Harmonic Oscillator. 138 Transition Amplitude Hermiticity.143 10 Matrix Element of a Physical Operator via Functional Integral 145 10.1 Matrix Representation of the Transition Amplitude of a Forced Harmonic Oscillator.147 10.1.1 Charged Particle Interaction with Phonons. 150 11 Path Integral Perturbation Theory 153 11.1 Time-Dependent Perturbation. 160 11.2 Transition Probability.163 11.3 Time-Energy Uncertainty Relation. 164 11.4 Density of Final State. 166 11.4.1 Transition Rate.166 11.5 Continuous Spectrum due to a Constant Perturbation.168 11.6 Harmonic Perturbation.169 12 Transition Matrix Element 173 13 Functional Derivative 179 13.1 Functional Derivative of
the Action Functional. 181 13.2 Functional Derivative and Matrix Element.183 14 Quantum Statistical Mechanics Functional Integral Approach 191 14.1 Introduction.191 14.2 Density Matrix.191 14.2.1 Partition Function. 191 14.3 Expectation Value of a Physical Observable. 192 14.4 Density Matrix.192 14.5 Density Matrix in the Energy Representation.194 15 Partition Function and Density Matrix Path Integral Representation 199 15.1 Density Matrix Path Integral Representation.199 15.1.1 Density Matrix Operator Average Value in Phase Space. 199 15.1.1.1 Generalized Gaussian Functional Path Integral in Phase Space.201 15.1.2 Density Matrix via Transition Amplitude.202
15.2 Partition Function in the Path Integral Representation. 205 15.3 Particle Interaction with a Driven or Forced Harmonic Oscillator: Partition Function.209
Contents viii 15.4 Free Particle Density Matrix and Partition Function. 121 15.5 Quantum Harmonic Oscillator Density Matrix and Partition Function. 214 16 Quasi-Classical Approximation in Quantum Statistical Mechanics 219 16.1 Centroid Effective Potential. 220 16.2 Expectation Value.225 17 Feynman Variational Method 18 Polaron Theory 237 18.1 Introduction. 237 18.2 Potaron Energy and Effective Mass.239 18.3 Functional Influence Phase. 241 18.3.1 Polaron Model Lagrangian.243 18.3.2 Polaron Partition Function.243 18.4 Influence Phase via Feynman Functional Integral in The Density Matrix Representation. 246 18.4.1 Expectation Value of a Physical
Quantity.246 18.4.1.1 Density Matrix.246 18.5 Full System Polaron Partition Function in a 3D Structure. 255 18.6 Model System Polaron Partition Function in a 3D Structure.256 18.7 Feynman Inequality and Generating Functional.257 18.8 Polaron Characteristics in a 3D Structure. 259 18.8.1 Polaron Asymptotic Characteristics. 264 18.9 Polaron Characteristics in a Quasi-ID Quantum Wire. 265 18.9.1 Hamiltonian of the Electron in a Quasi ID Quantum Wire.265 18.9.1.1 Lagrangian of the Electron in a Quasi-ID Quantum Wire. 266 18.9.1.2 Partition Function of the Electron in a Quasi-ID Quantum Wire.267 18.10 Polaron Generating Function. 269 18.11 Polaron Asymptotic Characteristics.270 18.12 Strong Coupling Regime Polaron Characteristics.273 18.13 Bipolaron Characteristics in
a Quasi-ID Quantum Wire. 276 18.13.1 Introduction. 276 18.13.2 Bipolaron Diagrammatic Representation.278 18.13.3 Bipolaron Lagrangian. 278 18.13.4 Bipolaron Equation of Motion.280 18.13.5 Transformation into Normal Coordinates.282 18.13.5.1 Diagonalization of the Lagrangian. 282 18.13.6 Bipolaron Partition Function. 283 18.13.7 Bipolaron Generating Function.285 18.13.8 Bipolaron Asymptotic Characteristics. 286 18.14 Polaron Characteristics in a Quasi-OD Spherical Quantum Dot. 289 18.14.1 Introduction.289 18.14.2 Polaron Lagrangian. 290 18.14.3 Normal
Modes.290 18.14.4 Lagrangian Diagonalization. 291 18.14.4.1 Transformation to Normal Coordinates. 291 18.14.5 Polaron Partition Function. 292 18.14.6 Generating Function.293 18.15 Bipolaron Characteristics in a Quasi-OD Spherical Quantum Dot.295 18.15.1 Introduction.295 18.15.2 Model Lagrangian. 296 229
Contents ix 18.15.3 Model Lagrangian.296 18.15.3.1 Equation of Motion and Normal Modes.296 18.15.4 Diagonalization of the Lagrangian.297 18.15.5 Partition Function.299 18.15.6 Full System Influence Phase. 300 18.16 Bipolaran Energy.300 18.16.1 Generating Function. 300 18.16.2 Bipolaran Characteristics.301 18.17 Polaran Characteristics in a Cylindrical Quantum Dot.304 18.17.1 System Hamiltonian. 304 18.17.2 Transformation to Normal Coordinates. 305 18.17.2.1 Lagrangian Diagonalization.305 18.17.3 Polaran Energy/Partition Function.306 18.17.4 Polaran
Generating Function. 307 18.17.5 Polaran Energy.308 18.18 Bipolaran Characteristics in a Cylindrical Quantum Dot. 310 18.18.1 System Hamiltonian. 310 18.18.1.1 Model System Action Functional.310 18.18.1.2 Equation of Motion / Normal Modes. 311 18.18.1.3 Lagrangian Diagonalization. 312 18.18.1.4 Bipolaran Partition Function. 312 18.18.1.5 Bipolaran Generating Function. 313 18.18.1.6 В ipolaron Energy.313 18.19 Polaran Characteristics in a Quasi-0D Cylindrical Quantum Dot with Asymmetrical Parabolic Potential.315 18.20 Polaran Energy.316 18.21 Bipolaran Characteristics in a Quasi-0D Cylindrical Quantum Dot with Asymmetrical Parabolic
Potential.320 18.22 Polaran in a Magnetic Field.324 19 Multiphoton Absorption by Polarons in a Spherical Quantum Dot 337 19.1 Theory of Multiphoton Absorption by Polarons.337 19.2 Basic Approximations.338 19.3 Absorption Coefficient.339 20 Polaronic Kinetics in a Spherical Quantum Dot 351 Kinetic Theory of Gases 365 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 Distribution Function.365 Principle of Detailed Equilibrium. 365 Transport Phenomenon and Boltzmann-Lorentz Kinetic Equation. 369 Transport Relaxation Time. 373 Boltzmann H-Theorem. 375 Thermal Conductivity.378
Diffusion.380 Electron-Phonon System Equation of Motion.386 References. 391 Index. .395 |
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| author | Fai, Lukong Cornelius 1961- |
| author_GND | (DE-588)1191949486 |
| author_facet | Fai, Lukong Cornelius 1961- |
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| callnumber-subject | QC - Physics |
| classification_rvk | UK 4500 |
| ctrlnum | (OCoLC)1261745035 (DE-599)KXP1738976254 |
| dewey-full | 530.14/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
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| dewey-search | 530.14/3 |
| dewey-sort | 3530.14 13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | First edition |
| format | Book |
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| id | DE-604.BV047338686 |
| illustrated | Illustrated |
| index_date | 2024-07-03T17:33:38Z |
| indexdate | 2024-07-10T09:09:23Z |
| institution | BVB |
| isbn | 9780367697853 9780367702991 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032741132 |
| oclc_num | 1261745035 |
| open_access_boolean | |
| owner | DE-703 DE-706 DE-11 |
| owner_facet | DE-703 DE-706 DE-11 |
| physical | xiv, 400 Seiten Illustrationen, Diagramme |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Fai, Lukong Cornelius 1961- Verfasser (DE-588)1191949486 aut Feynman path integrals in quantum mechanics and statistical physics Professor Lukong Cornelius Fai First edition Boca Raton ; London ; New York CRC Press 2021 xiv, 400 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seite 391-393 "This book provides an ideal introduction to the use of Feynman Path Integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations"-- Pfadintegral (DE-588)4173973-5 gnd rswk-swf Feynman integrals Quantum theory Statistical physics Pfadintegral (DE-588)4173973-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-003-14555-4 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032741132&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fai, Lukong Cornelius 1961- Feynman path integrals in quantum mechanics and statistical physics Pfadintegral (DE-588)4173973-5 gnd |
| subject_GND | (DE-588)4173973-5 |
| title | Feynman path integrals in quantum mechanics and statistical physics |
| title_auth | Feynman path integrals in quantum mechanics and statistical physics |
| title_exact_search | Feynman path integrals in quantum mechanics and statistical physics |
| title_exact_search_txtP | Feynman path integrals in quantum mechanics and statistical physics |
| title_full | Feynman path integrals in quantum mechanics and statistical physics Professor Lukong Cornelius Fai |
| title_fullStr | Feynman path integrals in quantum mechanics and statistical physics Professor Lukong Cornelius Fai |
| title_full_unstemmed | Feynman path integrals in quantum mechanics and statistical physics Professor Lukong Cornelius Fai |
| title_short | Feynman path integrals in quantum mechanics and statistical physics |
| title_sort | feynman path integrals in quantum mechanics and statistical physics |
| topic | Pfadintegral (DE-588)4173973-5 gnd |
| topic_facet | Pfadintegral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032741132&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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