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Quantum mechanics: concepts and applications

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1. Verfasser:	Zettili, Nouredine (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Chichester [u.a.] Wiley 2008
Ausgabe:	reprint.
Schlagworte:	Quantenmechanik Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIV, 649 S. Ill., graph. Darst.
ISBN:	9780471489443 9780471489436

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adam_text	Contents Preface xiii 1 Origins of Quantum Physics 1 1.1 Historical Note .................................. 1 1.2 Particle Aspect of Radiation ........................... 4 1.2.1 Blackbody Radiation ........................... 4 1.2.2 Photoelectric Effect ............................ 10 1.2.3 Compton Effect .............................. 13 1.2.4 Pair Production .............................. 15 1.3 Wave Aspect of Particles ............................. 17 1.3.1 de Broglie s Hypothesis: Matter Waves ................. 17 1.3.2 Experimental Confirmation of de Broglie s Hypothesis ......... 18 1.3.3 Matter Waves for Macroscopic Objects ................. 20 1.4 Particles versus Waves .............................. 21 1.4.1 Classical View of Particles and Waves .................. 21 1.4.2 Quantum View of Particles and Waves .................. 23 1.4.3 Wave-Particle Duality: Complementarity ................ 25 1.4.4 Principle of Linear Superposition .................... 26 1.5 Indeterministic Nature of the Microphysical World ............... 27 1.5.1 Heisenberg Uncertainty Principle .................... 27 1.5.2 Probabilistic Interpretation ........................ 29 1.6 Atomic Transitions and Spectroscopy ...................... 30 1.6.1 Rutherford Planetary Model of the Atom ................ 30 1.6.2 Bohr Model of the Hydrogen Atom ................... 30 1.7 Quantization Rules ................................ 36 1.8 Wave Packets ................................... 38 1.8.1 Localized Wave Packets ......................... 38 1.8.2 Wave Packets and the Uncertainty Relations ............... 41 1.8.3 Motion of Wave Packets ......................... 42 1.9 Concluding Remarks ............................... 53 1.10 Solved Problems ................................. 54 Exercises ........................................ 71 vi CONTENTS 2 Mathematical Tools of Quantum Mechanics 79 2.1 Introduction .................................... 79 2.2 The Hubert Space and Wave Functions ...................... 79 2.2.1 The Linear Vector Space ......................... 79 2.2.2 The Hubert Space ............................ 80 2.2.3 Dimension and Basis of a Vector Space ................. 81 2.2.4 Square-Integrable Functions: Wave Functions .............. 83 2.3 Dirac Notation .................................. 84 2.4 Operators ..................................... 88 2.4.1 General Definitions ............................ 88 2.4.2 Hermitian Adjoint ............................ 89 2.4.3 Projection Operators ........................... 91 2.4.4 Commutator Algebra ........................... 92 2.4.5 Uncertainty Relation between Two Operators .............. 94 2.4.6 Functions of Operators .......................... 95 2.4.7 Inverse and Unitary Operators ...................... 96 2.4.8 Eigenvalues and Eigenvectors of an Operator .............. 97 2.4.9 Infinitesimal and Finite Unitary Transformations ............ 100 2.5 Representation in Discrete Bases ......................... 102 2.5.1 Matrix Representation of Kets, Bras and Operators ........... 103 2.5.2 Change of Bases and Unitary Transformations ............. Ill 2.5.3 Matrix Representation of the Eigenvalue Problem ............ 114 2.6 Representation in Continuous Bases ....................... 117 2.6.1 General Treatment ............................ 117 2.6.2 Position Representation ......................... 119 2.6.3 Momentum Representation ........................ 120 2.6.4 Connecting the Position and Momentum Representations ........ 120 2.6.5 Parity Operator .............................. 124 2.7 Matrix and Wave Mechanics ........................... 126 2.7.1 Matrix Mechanics ............................ 126 2.7.2 Wave Mechanics ............................. 127 2.8 Concluding Remarks ............................... 128 2.9 Solved Problems ................................. 129 Exercises ........................................ 148 3 Postulates of Quantum Mechanics 157 3.1 Introduction .................................... 157 3.2 The Basic Postulates of Quantum Mechanics .................. 157 3.3 The State of a System ............................... 159 3.3.1 Probability Density ............................ 159 3.3.2 The Superposition Principle ....................... 160 3.4 Observables and Operators ............................ 162 3.5 Measurement in Quantum Mechanics ...................... 164 3.5.1 How Measurements Disturb Systems .................. 164 3.5.2 Expectation Values ............................ 165 3.5.3 Complete Sets of Commuting Operators ................. 167 3.5.4 Measurement and the Uncertainty Relations ............... 169 CONTENTS vii 3.6 Time Evolution of the System s State....................... 170 3.6.1 Time Evolution Operator ......................... 170 3.6.2 Stationary States: Time-Independent Potentials ............. 171 3.6.3 Schrödinger Equation and Wave Packets ................. 172 3.6.4 The Conservation of Probability ..................... 173 3.6.5 Time Evolution of Expectation Values .................. 174 3.7 Symmetries and Conservation Laws ....................... 175 3.7.1 Infinitesimal Unitary Transformations .................. 175 3.7.2 Finite Unitary Transformations ...................... 176 3.7.3 Symmetries and Conservation Laws ................... 177 3.8 Connecting Quantum to Classical Mechanics .................. 179 3.8.1 Poisson Brackets and Commutators ................... 179 3.8.2 The Ehrenfest Theorem .......................... 181 3.8.3 Quantum Mechanics and Classical Mechanics .............. 182 3.9 Solved Problems ................................. 183 Exercises ........................................ 199 4 One-Dimensional Problems 205 4.1 Introduction .................................... 205 4.2 Properties of One-Dimensional Motion ...................... 206 4.2.1 Discrete Spectrum (Bound States) .................... 206 4.2.2 Continuous Spectrum (Unbound States) ................. 207 4.2.3 Mixed Spectrum ............................. 207 4.2.4 Symmetric Potentials and Parity ..................... 207 4.3 The Free Particle: Continuous States ....................... 208 4.4 The Potential Step ................................. 210 4.5 The Potential Barrier and Well .......................... 213 4.5.1 The Case E > Vo ............................. 214 4.5.2 The Case E < Fo: Tunneling ...................... 216 4.5.3 The Tunneling Effect ........................... 219 4.6 The Infinite Square Well Potential ........................ 220 4.6.1 The Unsymmetric Square Well ...................... 220 4.6.2 The Symmetric Potential Well ...................... 223 4.7 The Finite Square Well Potential ......................... 224 4.7.1 The Scattering Solutions (E > Vo) .................... 224 4.7.2 The Bound State Solutions (0 < E < Vo) ................ 224 4.8 The Harmonic Oscillator ............................. 227 4.8.1 Energy Eigenvalues ............................ 229 4.8.2 Energy Eigenstates ............................ 231 4.8.3 Energy Eigenstates in Position Space .................. 231 4.8.4 The Matrix Representation of Various Operators ............ 234 4.8.5 Expectation Values of Various Operators ................ 235 4.9 Numerical Solution of the Schrödinger Equation ................. 236 4.9.1 Numerical Procedure ........................... 236 4.9.2 Algorithm ................................. 237 4.10 Solved Problems ................................. 239 Exercises ........................................ 263 viii CONTENTS 5 Angular Momentum 269 5.1 Introduction .................................... 269 5.2 Orbital Angular Momentum ........................... 269 5.3 General Formalism of Angular Momentum ................... 271 5.4 Matrix Representation of Angular Momentum .................. 276 5.5 Geometrical Representation of Angular Momentum ............... 279 5.6 Spin Angular Momentum ............................. 280 5.6.1 Experimental Evidence of the Spin .................... 280 5.6.2 General Theory of Spin .......................... 283 5.6.3 Spin 1/2 and the Pauli Matrices ..................... 284 5.7 Eigenfunctions of Orbital Angular Momentum .................. 287 5.7.1 Eigenfunctions and Eigenvalues of ¿z .................. 288 5.7.2 Eigenfunctions of I2 ........................... 289 5.7.3 Properties of the Spherical Harmonics .................. 292 5.8 Solved Problems ................................. 295 Exercises ........................................ 311 6 Three-Dimensional Problems 317 6.1 Introduction ....................................317 6.2 3D Problems in Cartesian Coordinates ......................317 6.2.1 General Treatment: Separation of Variables ...............317 6.2.2 The Free Particle .............................319 6.2.3 The Box Potential ............................320 6.2.4 The Harmonic Oscillator .........................322 6.3 3D Problems in Spherical Coordinates ......................324 6.3.1 Central Potential: General Treatment ..................324 6.3.2 The Free Particle in Spherical Coordinates ...............327 6.3.3 The Spherical Square Well Potential ...................329 6.3.4 The Isotropie Harmonic Oscillator ....................330 6.3.5 The Hydrogen Atom ...........................334 6.3.6 Effect of Magnetic Fields on Central Potentials .............348 6.4 Concluding Remarks ...............................351 6.5 Solved Problems .................................351 Exercises ........................................368 7 Rotations and Addition of Angular Momenta 373 7.1 Rotations in Classical Physics .......................... 373 7.2 Rotations in Quantum Mechanics ......................... 375 7.2.1 Infinitesimal Rotations .......................... 375 7.2.2 Finite Rotations .............................. 377 7.2.3 Properties of the Rotation Operator ................... 378 7.2.4 Euler Rotations .............................. 379 7.2.5 Representation of the Rotation Operator ................. З8О 7.2.6 Rotation Matrices and the Spherical Harmonics ............. 382 7.3 Addition of Angular Momenta .......................... 385 7.3.1 Addition of Two Angular Momenta: General Formalism ........ 385 7.3.2 Calculation oftheClebsch-Gordan Coefficients ............. 391 CONTENTS ix 7.3.3 Coupling of Orbital and Spin Angular Momenta ............ 397 7.3.4 Addition of More Than Two Angular Momenta ............. 401 7.3.5 Rotation Matrices for Coupling Two Angular Momenta ......... 402 7.3.6 Isospin .................................. 404 7.4 Scalar, Vector and Tensor Operators ....................... 407 7.4.1 Scalar Operators ............................. 408 7.4.2 Vector Operators ............................. 408 7.4.3 Tensor Operators: Reducible and Irreducible Tensors .......... 410 7.4.4 Wigner-Eckart Theorem for Spherical Tensor Operators ........ 412 7.5 Solved Problems ................................. 415 Exercises ........................................ 431 8 Identical Particles 437 8.1 Many-Particle Systems .............................. 437 8.1.1 Schrödinger Equation ........................... 437 8.1.2 Interchange Symmetry .......................... 439 8.1.3 Systems of Distinguishable Noninteracting Particles .......... 440 8.2 Systems of Identical Particles ........................... 442 8.2.1 Identical Particles in Classical and Quantum Mechanics ........ 442 8.2.2 Exchange Degeneracy .......................... 444 8.2.3 Symmetrization Postulate ........................ 445 8.2.4 Constructing Symmetric and Antisymmetric Functions ......... 446 8.2.5 Systems of Identical Noninteracting Particles .............. 446 8.3 The Pauli Exclusion Principle .......................... 449 8.4 The Exclusion Principle and the Periodic Table ................. 451 8.5 Solved Problems ................................. 457 Exercises ........................................ 466 9 Approximation Methods for Stationary States 469 9.1 Introduction .................................... 469 9.2 Time-Independent Perturbation Theory ...................... 470 9.2.1 Nondegenerate Perturbation Theory ................... 470 9.2.2 Degenerate Perturbation Theory ..................... 476 9.2.3 Fine Structure and the Anomalous Zeeman Effect ............ 479 9.3 The Variational Method .............................. 488 9.4 The Wentzel-Kramers-Brillouin Method .................... 495 9.4.1 General Formalism ............................ 495 9.4.2 Bound States for Potential Wells with No Rigid Walls ......... 498 9.4.3 Bound States for Potential Wells with One Rigid Wall ......... 504 9.4.4 Bound States for Potential Wells with Two Rigid Walls ......... 505 9.4.5 Tunneling through a Potential Barrier .................. 507 9.5 Concluding Remarks ............................... 510 9.6 Solved Problems ................................. 510 Exercises ........................................ 542 x CONTENTS 10 Time-Dependent Perturbation Theory 549 10.1 Introduction ....................................549 10.2 The Pictures of Quantum Mechanics .......................549 10.2.1 The Schrödinger Picture .........................550 10.2.2 The Heisenberg Picture ..........................550 10.2.3 The Interaction Picture ..........................551 10.3 Time-Dependent Perturbation Theory ......................552 10.3.1 Transition Probability ..........................554 10.3.2 Transition Probability for a Constant Perturbation ............555 10.3.3 Transition Probability for a Harmonic Perturbation ...........557 10.4 Adiabatic and Sudden Approximations ......................560 10.4.1 Adiabatic Approximation .........................560 10.4.2 Sudden Approximation ..........................561 10.5 Interaction of Atoms with Radiation .......................564 10.5.1 Classical Treatment of the Incident Radiation ..............565 10.5.2 Quantization of the Electromagnetic Field ................566 10.5.3 Transition Rates for Absorption and Emission of Radiation .......569 10.5.4 Transition Rates within the Dipole Approximation ...........570 10.5.5 The Electric Dipole Selection Rules ...................571 10.5.6 Spontaneous Emission ..........................572 10.6 Solved Problems .................................575 Exercises ........................................591 11 Scattering Theory 595 11.1 Scattering and Cross Section ...........................595 11.1.1 Connecting the Angles in the Lab and CM frames ............596 11.1.2 Connecting the Lab and CM Cross Sections ...............598 11.2 Scattering Amplitude of Spinless Particles ....................599 11.2.1 Scattering Amplitude and Differential Cross Section ..........601 11.2.2 Scattering Amplitude ...........................602 11.3 The Born Approximation .............................606 11.3.1 The First Born Approximation ......................606 11.3.2 Validity of the First Born Approximation ................607 11.4 Partial Wave Analysis ...............................609 11.4.1 Partial Wave Analysis for Elastic Scattering ...............609 11.4.2 Partial Wave Analysis for Inelastic Scattering ..............613 11.5 Scattering of Identical Particles ..........................614 11.6 Solved Problems .................................617 Exercises ........................................627 A The Delta Function 629 A. 1 One-Dimensional Delta Function ......................... 629 АЛЛ Various Definitions of the Delta Function ................ 629 A.1.2 Properties of the Delta Function ..................... 630 A.1.3 Derivative of the Delta Function ..................... 631 A.2 Three-Dimensional Delta Function ........................ 631 CONTENTS xi В Angular Momentum in Spherical Coordinates 633 B. 1 Derivation of Some General Relations ...................... 633 B.2 Gradient and Laplacian in Spherical Coordinates ................ 634 B.3 Angular Momentum in Spherical Coordinates .................. 635 С Computer Code for Solving the Schrödinger Equation 637 References 641 Index 643
adam_txt	Contents Preface xiii 1 Origins of Quantum Physics 1 1.1 Historical Note . 1 1.2 Particle Aspect of Radiation . 4 1.2.1 Blackbody Radiation . 4 1.2.2 Photoelectric Effect . 10 1.2.3 Compton Effect . 13 1.2.4 Pair Production . 15 1.3 Wave Aspect of Particles . 17 1.3.1 de Broglie's Hypothesis: Matter Waves . 17 1.3.2 Experimental Confirmation of de Broglie's Hypothesis . 18 1.3.3 Matter Waves for Macroscopic Objects . 20 1.4 Particles versus Waves . 21 1.4.1 Classical View of Particles and Waves . 21 1.4.2 Quantum View of Particles and Waves . 23 1.4.3 Wave-Particle Duality: Complementarity . 25 1.4.4 Principle of Linear Superposition . 26 1.5 Indeterministic Nature of the Microphysical World . 27 1.5.1 Heisenberg Uncertainty Principle . 27 1.5.2 Probabilistic Interpretation . 29 1.6 Atomic Transitions and Spectroscopy . 30 1.6.1 Rutherford Planetary Model of the Atom . 30 1.6.2 Bohr Model of the Hydrogen Atom . 30 1.7 Quantization Rules . 36 1.8 Wave Packets . 38 1.8.1 Localized Wave Packets . 38 1.8.2 Wave Packets and the Uncertainty Relations . 41 1.8.3 Motion of Wave Packets . 42 1.9 Concluding Remarks . 53 1.10 Solved Problems . 54 Exercises . 71 vi CONTENTS 2 Mathematical Tools of Quantum Mechanics 79 2.1 Introduction . 79 2.2 The Hubert Space and Wave Functions . 79 2.2.1 The Linear Vector Space . 79 2.2.2 The Hubert Space . 80 2.2.3 Dimension and Basis of a Vector Space . 81 2.2.4 Square-Integrable Functions: Wave Functions . 83 2.3 Dirac Notation . 84 2.4 Operators . 88 2.4.1 General Definitions . 88 2.4.2 Hermitian Adjoint . 89 2.4.3 Projection Operators . 91 2.4.4 Commutator Algebra . 92 2.4.5 Uncertainty Relation between Two Operators . 94 2.4.6 Functions of Operators . 95 2.4.7 Inverse and Unitary Operators . 96 2.4.8 Eigenvalues and Eigenvectors of an Operator . 97 2.4.9 Infinitesimal and Finite Unitary Transformations . 100 2.5 Representation in Discrete Bases . 102 2.5.1 Matrix Representation of Kets, Bras and Operators . 103 2.5.2 Change of Bases and Unitary Transformations . Ill 2.5.3 Matrix Representation of the Eigenvalue Problem . 114 2.6 Representation in Continuous Bases . 117 2.6.1 General Treatment . 117 2.6.2 Position Representation . 119 2.6.3 Momentum Representation . 120 2.6.4 Connecting the Position and Momentum Representations . 120 2.6.5 Parity Operator . 124 2.7 Matrix and Wave Mechanics . 126 2.7.1 Matrix Mechanics . 126 2.7.2 Wave Mechanics . 127 2.8 Concluding Remarks . 128 2.9 Solved Problems . 129 Exercises . 148 3 Postulates of Quantum Mechanics 157 3.1 Introduction . 157 3.2 The Basic Postulates of Quantum Mechanics . 157 3.3 The State of a System . 159 3.3.1 Probability Density . 159 3.3.2 The Superposition Principle . 160 3.4 Observables and Operators . 162 3.5 Measurement in Quantum Mechanics . 164 3.5.1 How Measurements Disturb Systems . 164 3.5.2 Expectation Values . 165 3.5.3 Complete Sets of Commuting Operators . 167 3.5.4 Measurement and the Uncertainty Relations . 169 CONTENTS vii 3.6 Time Evolution of the System's State. 170 3.6.1 Time Evolution Operator . 170 3.6.2 Stationary States: Time-Independent Potentials . 171 3.6.3 Schrödinger Equation and Wave Packets . 172 3.6.4 The Conservation of Probability . 173 3.6.5 Time Evolution of Expectation Values . 174 3.7 Symmetries and Conservation Laws . 175 3.7.1 Infinitesimal Unitary Transformations . 175 3.7.2 Finite Unitary Transformations . 176 3.7.3 Symmetries and Conservation Laws . 177 3.8 Connecting Quantum to Classical Mechanics . 179 3.8.1 Poisson Brackets and Commutators . 179 3.8.2 The Ehrenfest Theorem . 181 3.8.3 Quantum Mechanics and Classical Mechanics . 182 3.9 Solved Problems . 183 Exercises . 199 4 One-Dimensional Problems 205 4.1 Introduction . 205 4.2 Properties of One-Dimensional Motion . 206 4.2.1 Discrete Spectrum (Bound States) . 206 4.2.2 Continuous Spectrum (Unbound States) . 207 4.2.3 Mixed Spectrum . 207 4.2.4 Symmetric Potentials and Parity . 207 4.3 The Free Particle: Continuous States . 208 4.4 The Potential Step . 210 4.5 The Potential Barrier and Well . 213 4.5.1 The Case E > Vo . 214 4.5.2 The Case E < Fo: Tunneling . 216 4.5.3 The Tunneling Effect . 219 4.6 The Infinite Square Well Potential . 220 4.6.1 The Unsymmetric Square Well . 220 4.6.2 The Symmetric Potential Well . 223 4.7 The Finite Square Well Potential . 224 4.7.1 The Scattering Solutions (E > Vo) . 224 4.7.2 The Bound State Solutions (0 < E < Vo) . 224 4.8 The Harmonic Oscillator . 227 4.8.1 Energy Eigenvalues . 229 4.8.2 Energy Eigenstates . 231 4.8.3 Energy Eigenstates in Position Space . 231 4.8.4 The Matrix Representation of Various Operators . 234 4.8.5 Expectation Values of Various Operators . 235 4.9 Numerical Solution of the Schrödinger Equation . 236 4.9.1 Numerical Procedure . 236 4.9.2 Algorithm . 237 4.10 Solved Problems . 239 Exercises . 263 viii CONTENTS 5 Angular Momentum 269 5.1 Introduction . 269 5.2 Orbital Angular Momentum . 269 5.3 General Formalism of Angular Momentum . 271 5.4 Matrix Representation of Angular Momentum . 276 5.5 Geometrical Representation of Angular Momentum . 279 5.6 Spin Angular Momentum . 280 5.6.1 Experimental Evidence of the Spin . 280 5.6.2 General Theory of Spin . 283 5.6.3 Spin 1/2 and the Pauli Matrices . 284 5.7 Eigenfunctions of Orbital Angular Momentum . 287 5.7.1 Eigenfunctions and Eigenvalues of ¿z . 288 5.7.2 Eigenfunctions of I2 . 289 5.7.3 Properties of the Spherical Harmonics . 292 5.8 Solved Problems . 295 Exercises . 311 6 Three-Dimensional Problems 317 6.1 Introduction .317 6.2 3D Problems in Cartesian Coordinates .317 6.2.1 General Treatment: Separation of Variables .317 6.2.2 The Free Particle .319 6.2.3 The Box Potential .320 6.2.4 The Harmonic Oscillator .322 6.3 3D Problems in Spherical Coordinates .324 6.3.1 Central Potential: General Treatment .324 6.3.2 The Free Particle in Spherical Coordinates .327 6.3.3 The Spherical Square Well Potential .329 6.3.4 The Isotropie Harmonic Oscillator .330 6.3.5 The Hydrogen Atom .334 6.3.6 Effect of Magnetic Fields on Central Potentials .348 6.4 Concluding Remarks .351 6.5 Solved Problems .351 Exercises .368 7 Rotations and Addition of Angular Momenta 373 7.1 Rotations in Classical Physics . 373 7.2 Rotations in Quantum Mechanics . 375 7.2.1 Infinitesimal Rotations . 375 7.2.2 Finite Rotations . 377 7.2.3 Properties of the Rotation Operator . 378 7.2.4 Euler Rotations . 379 7.2.5 Representation of the Rotation Operator . З8О 7.2.6 Rotation Matrices and the Spherical Harmonics . 382 7.3 Addition of Angular Momenta . 385 7.3.1 Addition of Two Angular Momenta: General Formalism . 385 7.3.2 Calculation oftheClebsch-Gordan Coefficients . 391 CONTENTS ix 7.3.3 Coupling of Orbital and Spin Angular Momenta . 397 7.3.4 Addition of More Than Two Angular Momenta . 401 7.3.5 Rotation Matrices for Coupling Two Angular Momenta . 402 7.3.6 Isospin . 404 7.4 Scalar, Vector and Tensor Operators . 407 7.4.1 Scalar Operators . 408 7.4.2 Vector Operators . 408 7.4.3 Tensor Operators: Reducible and Irreducible Tensors . 410 7.4.4 Wigner-Eckart Theorem for Spherical Tensor Operators . 412 7.5 Solved Problems . 415 Exercises . 431 8 Identical Particles 437 8.1 Many-Particle Systems . 437 8.1.1 Schrödinger Equation . 437 8.1.2 Interchange Symmetry . 439 8.1.3 Systems of Distinguishable Noninteracting Particles . 440 8.2 Systems of Identical Particles . 442 8.2.1 Identical Particles in Classical and Quantum Mechanics . 442 8.2.2 Exchange Degeneracy . 444 8.2.3 Symmetrization Postulate . 445 8.2.4 Constructing Symmetric and Antisymmetric Functions . 446 8.2.5 Systems of Identical Noninteracting Particles . 446 8.3 The Pauli Exclusion Principle . 449 8.4 The Exclusion Principle and the Periodic Table . 451 8.5 Solved Problems . 457 Exercises . 466 9 Approximation Methods for Stationary States 469 9.1 Introduction . 469 9.2 Time-Independent Perturbation Theory . 470 9.2.1 Nondegenerate Perturbation Theory . 470 9.2.2 Degenerate Perturbation Theory . 476 9.2.3 Fine Structure and the Anomalous Zeeman Effect . 479 9.3 The Variational Method . 488 9.4 The Wentzel-Kramers-Brillouin Method . 495 9.4.1 General Formalism . 495 9.4.2 Bound States for Potential Wells with No Rigid Walls . 498 9.4.3 Bound States for Potential Wells with One Rigid Wall . 504 9.4.4 Bound States for Potential Wells with Two Rigid Walls . 505 9.4.5 Tunneling through a Potential Barrier . 507 9.5 Concluding Remarks . 510 9.6 Solved Problems . 510 Exercises . 542 x CONTENTS 10 Time-Dependent Perturbation Theory 549 10.1 Introduction .549 10.2 The Pictures of Quantum Mechanics .549 10.2.1 The Schrödinger Picture .550 10.2.2 The Heisenberg Picture .550 10.2.3 The Interaction Picture .551 10.3 Time-Dependent Perturbation Theory .552 10.3.1 Transition Probability .554 10.3.2 Transition Probability for a Constant Perturbation .555 10.3.3 Transition Probability for a Harmonic Perturbation .557 10.4 Adiabatic and Sudden Approximations .560 10.4.1 Adiabatic Approximation .560 10.4.2 Sudden Approximation .561 10.5 Interaction of Atoms with Radiation .564 10.5.1 Classical Treatment of the Incident Radiation .565 10.5.2 Quantization of the Electromagnetic Field .566 10.5.3 Transition Rates for Absorption and Emission of Radiation .569 10.5.4 Transition Rates within the Dipole Approximation .570 10.5.5 The Electric Dipole Selection Rules .571 10.5.6 Spontaneous Emission .572 10.6 Solved Problems .575 Exercises .591 11 Scattering Theory 595 11.1 Scattering and Cross Section .595 11.1.1 Connecting the Angles in the Lab and CM frames .596 11.1.2 Connecting the Lab and CM Cross Sections .598 11.2 Scattering Amplitude of Spinless Particles .599 11.2.1 Scattering Amplitude and Differential Cross Section .601 11.2.2 Scattering Amplitude .602 11.3 The Born Approximation .606 11.3.1 The First Born Approximation .606 11.3.2 Validity of the First Born Approximation .607 11.4 Partial Wave Analysis .609 11.4.1 Partial Wave Analysis for Elastic Scattering .609 11.4.2 Partial Wave Analysis for Inelastic Scattering .613 11.5 Scattering of Identical Particles .614 11.6 Solved Problems .617 Exercises .627 A The Delta Function 629 A. 1 One-Dimensional Delta Function . 629 АЛЛ Various Definitions of the Delta Function . 629 A.1.2 Properties of the Delta Function . 630 A.1.3 Derivative of the Delta Function . 631 A.2 Three-Dimensional Delta Function . 631 CONTENTS xi В Angular Momentum in Spherical Coordinates 633 B. 1 Derivation of Some General Relations . 633 B.2 Gradient and Laplacian in Spherical Coordinates . 634 B.3 Angular Momentum in Spherical Coordinates . 635 С Computer Code for Solving the Schrödinger Equation 637 References 641 Index 643
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spelling	Zettili, Nouredine Verfasser aut Quantum mechanics concepts and applications Nouredine Zettili reprint. Chichester [u.a.] Wiley 2008 XIV, 649 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantenmechanik (DE-588)4047989-4 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Quantenmechanik (DE-588)4047989-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016742179&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Zettili, Nouredine Quantum mechanics concepts and applications Quantenmechanik (DE-588)4047989-4 gnd
subject_GND	(DE-588)4047989-4 (DE-588)4123623-3
title	Quantum mechanics concepts and applications
title_auth	Quantum mechanics concepts and applications
title_exact_search	Quantum mechanics concepts and applications
title_exact_search_txtP	Quantum mechanics concepts and applications
title_full	Quantum mechanics concepts and applications Nouredine Zettili
title_fullStr	Quantum mechanics concepts and applications Nouredine Zettili
title_full_unstemmed	Quantum mechanics concepts and applications Nouredine Zettili
title_short	Quantum mechanics
title_sort	quantum mechanics concepts and applications
title_sub	concepts and applications
topic	Quantenmechanik (DE-588)4047989-4 gnd
topic_facet	Quantenmechanik Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016742179&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT zettilinouredine quantummechanicsconceptsandapplications

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