Introduction to quantum mechanics:
"Quantum mechanics is a subfield of physics that studies how the universe works at atomic and subatomic levels. It is an essential part of undergraduate and graduate courses in physics and undergraduate engineering courses in India. This book comes from the desk of authors who have decades of g...
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY ; Portr Melbourne, Australia ; New Delhi, India
Cambridge University Press
2023
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Zusammenfassung: | "Quantum mechanics is a subfield of physics that studies how the universe works at atomic and subatomic levels. It is an essential part of undergraduate and graduate courses in physics and undergraduate engineering courses in India. This book comes from the desk of authors who have decades of graduate-level teaching experience in quantum mechanics. It covers the syllabus requirements set forth by the University Grants Commission (UGC), India, and has additional several unique features that will set it apart. It introduces the students to vector space in the beginning to give a comprehensive idea of the mathematics involved in the concepts, has separate appendices emphasizing the techniques of differential equations, and covers applications of quantum mechanics related to atomic physics, condensed matter physics, particle physics, and so on. The text is carefully designed and is not completely mathematical; it gives equal emphasis to the discussions around physics and creates a nice balance. The book will be suitable for both undergraduate and graduate students taking courses in physics and chemistry. Several advanced topics have been covered in this book. They are expected to be beneficial particularly to graduate students and researchers"-- |
Beschreibung: | xxii, 501 Seiten Illustrationen, Diagramme |
ISBN: | 9781009338424 |
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520 | 3 | |a "Quantum mechanics is a subfield of physics that studies how the universe works at atomic and subatomic levels. It is an essential part of undergraduate and graduate courses in physics and undergraduate engineering courses in India. This book comes from the desk of authors who have decades of graduate-level teaching experience in quantum mechanics. It covers the syllabus requirements set forth by the University Grants Commission (UGC), India, and has additional several unique features that will set it apart. It introduces the students to vector space in the beginning to give a comprehensive idea of the mathematics involved in the concepts, has separate appendices emphasizing the techniques of differential equations, and covers applications of quantum mechanics related to atomic physics, condensed matter physics, particle physics, and so on. The text is carefully designed and is not completely mathematical; it gives equal emphasis to the discussions around physics and creates a nice balance. The book will be suitable for both undergraduate and graduate students taking courses in physics and chemistry. Several advanced topics have been covered in this book. They are expected to be beneficial particularly to graduate students and researchers"-- | |
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Contents List of Figures xv List of Tables xvii Notation xix Preface xxi Part One: Formalism 1 1 Uncertainty 3 Classical mechanics. Wave-particle duality. The uncertainty principle. Time-energy uncertainty. Interference experiments. 3 5 7 11 12 1.1 1.2 1.3 1.4 1.5 2 State vectors 15 Introduction. Vector spaces . 2.2.1 Definition. 2.2.2 Linear independence andbasis. Vector spaces with extra structure. 2.3.1 Normed vector spaces. 2.3.2 Inner product spaces. Orthogonality, normalization, and completeness. States as vectors. Operators on vector spaces. Eigenvalues and
eigenvectors of operators. 2.7.1 Definition and algorithm . 2.7.2 Linear independenceof eigenvectors. 2.7.3 Eigenvectors of commutingoperators . 15 16 16 19 20 20 21 24 27 28 33 33 35 36 2.1 2.2 2.3 2.4 2.5 2.6 2.7 vii
Contents viii 2.8 Adjoint of an operator . 2.8.1 Definition. 2.8.2 Normal operators . 2.9 Hermitian operators. 2.9.1 Definition and basic properties. 2.9.2 Eigenvalues and eigenvectors. 2.9.3 Probabilistic interpretation of state vectors. 2.9.4 A relation between standard deviations. 2.9.5 Importance of Hermitian operators. 2.10 Unitary operators. 2.11 Basis and basis-independence . 08 33 39 43 43 45 48 49 50 53 3 Quantum dynamics-------------------------------------------------------------- 56 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Quantum bracket. Heisenberg equation. Schrödinger equation. Hilbert space. 3.4.1 What kind of a vector space
do weneed?. 3.4.2 Cauchy sequences andconvergent sequences. 3.4.3 Sequences in a vector space. Coordinate representation. 3.5.1 The wavefunction. 3.5.2 Probabilistic interpretation. 3.5.3 Square integrability of wavefunctions. 3.5.4 Momentum operator. 3.5.5 Schrödinger equation . 3.5.6 Probability current. Hermiticity of the momentum operator. Momentum representation. Another look at time-energy uncertainty. 3.8.1 Is time an operator?. 3.8.2 Uncertainty through any operator. 56 61 62 63 63 63 65 66 67 69 70 71 73 75 76 77 79 79 81 4 Time evolution of quantum systems 82 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Heisenberg equations and classical mechanics. Formal solutions of the basic equations. Stationary states
. Equivalence of Schrödinger and Heisenbergpictures. Interaction picture . Behavior of basis states. Density matrix. 4.7.1 Definition and formalism. 82 84 86 87 90 92 95 95
Contents 4.8 ix 4.7.2 An example. 98 4.7.3 Mixedstates. 100 Coherence vector. 101 5Symmetry 105 5.1 Symmetry and conservation. 105 5.2 Symmetry and degeneracy.108 5.3 Symmetry and group. 109 5.3.1 Definition of a group. 109 5.3.2 Symmetry group.110 5.4 Some important discrete groups. Ill 5.4.1 Parity. Ш 5.4.2 Exchange symmetry.112 5.4.3 Time reversal.113 5.5 Group representations . 117 5.5.1 Some examples as starters. 117 5.5.2 States and symmetry operators. 121 5.5.3 Reducible and irreducible representations. 122 5.5.4
Differential representations. 123 5.6 Generators of group elements . 124 5.6.1 Generators of discrete groups. 124 5.6.2 Generators of Lie groups.126 5.7 Important continuous groups. 127 5.7.1 The translation group. 127 5.7.2 The rotation group. 129 Part Two: Exact solutions 6 The 6.1 6.2 6.3 6.4 6.5 6.6 133 free particle_ —_ 135 Solution of free Schrödinger equation. 135 Wavepacket. 136 Spreading of wavepacket.138 Propagator. 141 Path integral formalism. 144 Interference experiments.147 7 Exactly solvable problems in one dimension 152 7.1 Stationary states .
152 7.2 Particle in a box. 153 7.3 Some general features. 156 7.4 Square-well potential. 159
Contents X 7.5 7.6 Square potential barrier . Ιθ2 Spike potential. ^θθ 7.6.1 General features.Ιθθ 7.6.2 Bound state in a well.1θ8 7.6.3 Reflection and transmission at a barrier. 168 7.7 Simple harmonic oscillator.Ιθθ 7.7.1 Coordinate space solution. 169 7.7.2 Solution by operator method. 172 7.8 Particle on a lattice. 175 8 Angular momentum _ _ 180 8.1 8.2 8.3 General considerations. 180 Coordinate representation. 186 Spin 1/2 algebra. 191 8.3.1 Basic formalism .191 8.3.2 Some applications.194 8.4 Higher matrix
representations. 196 8.4.1 Angular momentum matrices . . . . 197 8.4.2 Wigner matrices.198 8.5 Angular momentum and time-reversal transformation. 200 8.5.1 Explicit form of the time-reversal operator. 200 8.5.2 Phases. 202 8.6 Addition of angular momenta. 204 8.6.1 Relation between the states in the two bases. 204 8.6.2 Clebsch-Gordan coefficients. 207 8.6.3 Orthogonality and recursion relations. 210 8.7 Tensor operators. 212 8.7.1 Definition and properties. 213 8.7.2 Connection with Cartesian components of tensors.215 8.7.3 Wigner-Eckart theorem. 217 9 Exactly solvable problems in three dimensions 219 9.1 9.2 9.3 9.4 9.5 9.6 Generalities. 219 Particle in a 3D box. 219 3D
problems with central potentials.221 9.3.1 The eigenvalue equation.221 9.3.2 Degeneracy and conservation. 224 Particle in a spherical potential well.226 9.4.1 Infinite well. 227 9.4.2 Finite well . 228 Two-particle systems. 230 Hydrogen atom. 231
Contents 9.7 9.8 xi 9.6.1 The potential. 231 9.6.2 Solution of the differential equation. 232 9.6.3 Spectral lines of hydrogen. 237 9.6.4 Nature of the wavefunctions. 237 9.6.5 Degeneracy of eigenvalues. 242 9.6.6 A hint from classical physics. 242 9.6.7 Alternative method for findingenergy eigenvalues.245 3D isotropic oscillator. 249 Cooper problem.249 10 Particles in magnetic fields 10.1 10.2 10.3 10.4 10.5 10.6 10.7 253 The Hamiltonian.253 Landau levels. 256 10.2.1 Energy eigenvalues and eigenfunctions. 257 10.2.2 An alternative method. 259 10.2.3 2D particle in orthogonal magnetic field. 260 Gauge invariance.262 Aharonov-Bohm
effect. 266 Interactions with spin. 268 10.5.1 Interaction Hamiltonian. 268 10.5.2 Spin precession. 269 Stern-Gerlach experiment. 271 Effect of magnetic field for particles in a 2Dlattice. 273 Part Three: Approximations 11 Approximation methods 279 281 11.1 Variational method. 281 11.1.1 The method . 281 11.1.2 Examples.283 11.2 Non-degenerate perturbation theory. 285 11.2.1 The method . 285 11.2.2 Examples.288 11.3 Degenerate perturbation theory. 291 11.3.1 The method . 291 11.3.2 Examples.293 11.4 WKB
approximation.295 11.4.1 The method . 295 11.4.2 Examples. 300 12 Time-dependent problems 305
xjî Contents 12.1 12.2 12.3 12.4 General formulation.305 Time-dependent two-level system. 307 Level crossing. 311 Time-dependent perturbation theory. 315 12.4.1 Formalism .315 12.4.2 Transition rates .318 12.4.3 Harmonic perturbation. 320 12.5 Periodic drive: Floquet analysis. 322 13 Scattering theory 328 13.1 13.2 13.3 13.4 13.5 Lippmann-Schwinger formalism. 328 Scattering cross-section. 333 Born approximation. 337 Partial wave analysis. 339 Coulomb scattering. 345 Part Four: Advanced topics 14 Identical particles 14.1 14.2 14.3 351 Permutation symmetry. 351 Bosons and
fermions.353 Scattering of identical particles .356 15 Relativistic corrections 15.1 15.2 15.3 15.4 15.5 15.6 349 360 Conflict between relativity and quantum mechanics.360 Dirac Hamiltonian. 361 Spin . 364 Magnetic moment. 366 Dirac particle in a central potential. 368 Further prospects. 371 16 Interpretation of quantummechanics 374 Waves vs particles. 374 Collapse of a wavefunction. 376 EPR paradox. 376 Entanglement. 378 When does a measurement end?. 382 16.5.1 A generic description of paradoxes. 382 16.5.2 Schrôdinger cat
paradox. 383 16.6 Searching for answers. 384 16.6.1 When does collapse occur?. 384 16.6.2 A matter of size?. _. 385 16.1 16.2 16.3 16.4 16.5
Contents 16.7 xiii 16.6.3 Many universes? . 385 16.6.4 Hidden variables? . 385 Bell inequalities.386 17 Miscellaneous topics 391 17.1 Coherent states. 391 17.2 Pancharatnam-Berry phase . 396 17.3 Supersymmetric methods. 399 17.4 Lower-dimensional systems with linear Hamiltonians. 406 17.5 The path integral formulation revisited. 411 17.6 Non-Hermitian quantum mechanics. 416 17.6.1 General formulation. 416 17.6.2 A two-level system asexample. 419 17.6.3 PT-symmetric Hamiltonians . 420 Part Five: Appendices A Delta function 423 425 В Solution of second-order differential equations 429 B.l General considerations. 429 B.2 Equations with constant coefficients. 431 B.3 Checking the asymptotic
behavior. 432 B.4 Series solution at ordinary points. 434 B.4.1 General formulation. 434 B.4.2 The harmonic oscillator equation.436 B.5 Obtaining one solution from another . 436 B.6 Solution at regular singular points. 438 B.6.1 Frobenius’ method for power series solutions. 438 B.6.2 A simple example . 440 B.6.3 Possibility of problems with series solutions. 442 B.6.4 A variety of examples. 445 B.6.5 Revisiting ordinary points. 450 C Special functions 452 C.l Hermite equation. 452 C.2 Legendre equation. 454 C.3 Associated Legendre equation.457 C.4 Airy equation. 459 C.5 Bessel equation. 460 C.6
Spherical Bessel equation. 463 C.7 Modified Bessel equation. 466
xiv Contents C.8 C.9 C.10 C.ll Laguerre equation. 467 Generalized Laguerre equation. 468 Hypergeometric equation. 469 Confluent hypergeometric equation.471 D Further properties of special functions--------------------------------------- 473 D.l Generating functions. 473 D.2 Recurrence relations. 477 D.3 Orthogonality of special functions. 480 D.4 Asymptotic expansions of special functions. 484 D.4.1 Spherical Bessel functions. 484 D.4.2 Bessel functions . 485 D.4.3 Airy function. 485 D.4.4 Confluent hypergeometric functions. 486 D.4.5 General comments. 486 E Saddle-point method 487 E.l Outline of the method .487 E.2 Airy function
. 490 E.3 Bessel functions. 493 Index 495 |
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spelling | Sengupta, Krishnendu Verfasser (DE-588)1313609269 aut Introduction to quantum mechanics Krishnendu Sengupta, Palash B. Pal Cambridge, United Kingdom ; New York, NY ; Portr Melbourne, Australia ; New Delhi, India Cambridge University Press 2023 xxii, 501 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier "Quantum mechanics is a subfield of physics that studies how the universe works at atomic and subatomic levels. It is an essential part of undergraduate and graduate courses in physics and undergraduate engineering courses in India. This book comes from the desk of authors who have decades of graduate-level teaching experience in quantum mechanics. It covers the syllabus requirements set forth by the University Grants Commission (UGC), India, and has additional several unique features that will set it apart. It introduces the students to vector space in the beginning to give a comprehensive idea of the mathematics involved in the concepts, has separate appendices emphasizing the techniques of differential equations, and covers applications of quantum mechanics related to atomic physics, condensed matter physics, particle physics, and so on. The text is carefully designed and is not completely mathematical; it gives equal emphasis to the discussions around physics and creates a nice balance. The book will be suitable for both undergraduate and graduate students taking courses in physics and chemistry. Several advanced topics have been covered in this book. They are expected to be beneficial particularly to graduate students and researchers"-- Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantum theory / Textbooks Quantum theory / Mathematics / Textbooks Quantum theory Quantenmechanik (DE-588)4047989-4 s Quantentheorie (DE-588)4047992-4 s DE-604 Pal, Palash B. 1955- Verfasser (DE-588)13127290X aut Erscheint auch als Online-Ausgabe 978-1-009-33843-1 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=034749151&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Sengupta, Krishnendu Pal, Palash B. 1955- Introduction to quantum mechanics Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
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title | Introduction to quantum mechanics |
title_auth | Introduction to quantum mechanics |
title_exact_search | Introduction to quantum mechanics |
title_exact_search_txtP | Introduction to quantum mechanics |
title_full | Introduction to quantum mechanics Krishnendu Sengupta, Palash B. Pal |
title_fullStr | Introduction to quantum mechanics Krishnendu Sengupta, Palash B. Pal |
title_full_unstemmed | Introduction to quantum mechanics Krishnendu Sengupta, Palash B. Pal |
title_short | Introduction to quantum mechanics |
title_sort | introduction to quantum mechanics |
topic | Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
topic_facet | Quantentheorie Quantenmechanik |
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