高等量子力学简明教程 英文版PDF|Epub|txt|kindle电子书版本下载

高等量子力学简明教程 英文版PDF格式电子书版下载

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Chapter 1 Quantum states and physical quantities1

1.1 Quantum states as linear vectors in Hilbert space1

1.1.1 Quantum states as linear vectors1

1.1.2 Axiom of quantum mechanics concerning quantum states2

1.2 Physical quantities as operators in Hilbert space3

1.2.1 Eigenvalue and eigenvector of Hermitian operator3

1.2.2 Orthogonal-normalization condition of eigenvectors6

1.2.3 Axiom of quantum mechanics concerning physical quantities7

1.2.4 Completeness condition of eigenvector system8

1.2.5 Projection operator9

1.2.6 Density operator Pure state and mixed state10

1.3 Representation13

1.3.1 Definition of representation13

1.3.2 Representation transformation15

1.3.3 Enter in and escape from a representation16

1.3.4 Invariances of representation transformation16

1.4 Operators as non-commuting quantities17

1.4.1 Simultaneous measurability of physical quantities17

1.4.2 Commutator algebra17

1.4.3 Function of operator19

1.5 Unitary transformation Generator of continuous transformation20

1.5.1 Similar transformation and unitary transformation20

1.5.2 Relation between unitary operator and Hermitian operator22

1.5.3 Continuous transformation Generator23

1.5.4 Space displacement Momentum25

1.5.5 Space rotation Angular momentum26

Chapter 2 Time evolution of microscopic system Schr？dinger equation and propagator29

2.1 Time evolution in coordinate representation29

2.2 Time evolution operator in Hilbert space32

2.3 Picture in quantum mechanics33

2.3.1 Definition of picture and picture-transform in quantum mechanics33

2.3.2 Schr？dinger picture and Heisenberg picture35

2.3.3 Interaction picture36

2.4 Time evolution in the form of path integral40

2.4.1 Functional integral formula for propagator40

2.4.2 Functional integral as limit of multiple-integral42

2.4.3 Functional integral as sum over path43

2.4.4 Path-integral of Gaussian type47

2.4.5 From path integral to Schr？dinger equation48

2.5 Diffraction phenomena in quantum mechanics49

2.5.1 The role of phase in quantum mechanics49

2.5.2 Double-slot diffraction50

2.5.3 Aharonov-Bohm effect Magnetic-flux quantum52

2.6 Symmetry of microscopic system and conservation of physical quantity54

2.6.1 Symmetry of microscopic system54

2.6.2 Conservation of physical quantity55

2.6.3 Parity55

2.6.4 Time reversal56

Chapter 3 Angular momentum59

3.1 General solution of the eigenvalue problem of angular momentum59

3.1.1 The procedure for solving eigenvalue problem directly in Hilbert space60

3.1.2 Solution of the eigenvalue problem of angular momentum60

3.2 Two kinds of angular momentum63

3.2.1 Orbital angular momentum63

3.2.2 Spin64

3.3 Spin 1/267

3.3.1 Properties of Pauli matrix68

3.3.2 Density matrix of spin 1/2 state Polarization vector72

3.4 Representation of angular momentum76

3.4.1 Reducible and irreducible representations76

3.4.2 Irreducible tensor operator77

3.4.3 Property of D function78

3.5 Addition of angular momentum Clebsch-Gordan coefficients79

3.5.1 Addition of angular momentum79

3.5.2 Clebsch-Gordan coefficients85

3.5.3 Addition of D function87

Chapter 4 Multi-particle system89

4.1 Axiom on indistinguishability of identical particles89

4.2 Fock representation of multi-particle state——Discrete spectrum90

4.2.1 The representation basis90

4.2.2 Basic operators91

4.2.3 Action of basic operators on representation basis95

4.2.4 Representation-and canonical-transformations of annihilation and creation operators96

4.2.5 Operators of physical quantities in multi-particle system98

4.3 Fock representation for continuous spectrum100

4.3.1 Second quantization102

4.4 Time evolution in Fock representation104

4.5 Theory of superconductivity104

4.5.1 The BCS theory of superconductivity106

4.6 Two-state system111

4.6.1 Two-electron system111

4.6.2 Quantum bit Bell inequality113

Chapter 5 Uncertainty relation Coherent state119

5.1 Uncertainty relation Minimum-uncertainty state121

5.1.1 Uncertainty relation121

5.1.2 Minimum-uncertainty state122

5.1.3 Schwartz inequality124

5.2 Harmonic oscillator125

5.2.1 Solution of eigenvalue problem125

5.2.2 Time evolution of harmonic oscillator in Heisenberg picture127

5.3 Coherent state127

5.3.1 Definition of coherent state127

5.3.2 Properties of coherent state128

5.3.3 Representation with coherent states as basis131

5.3.4 Production of coherent state134

5.3.5 Coherent state in coordinate representation138

5.3.6 Displacement,rotation and squeeze operators for coherent states139

Chapter 6 One-dimensional problem Bound states and resonances145

6.1 Three-dimensional scattering and one-dimensional transmission and reflection145

6.2 Piecewise constant potential148

6.2.1 Potential box149

6.2.2 Rectangular potential well150

6.3 Poles of scattering amplitude in the complex Eplane154

6.3.1 Scattering resonance154

6.3.2 Poles of scattering amplitude on negative E axis Discrete energy levels155

6.3.3 Poles of scattering amplitude in complex E plane Breit-Wigner formula156

6.4 Space-time evolution of one-dimensional scattering157

6.4.1 Wave packet158

6.4.2 One-dimensional wave packet scattering159

6.4.3 Energy-time uncertainty relation161

6.5 Slowly-varying potential Semi-classical(WKB)approximation162

6.5.1 Canonical and path-integral quantizations162

6.5.2 The semi-classical approximation(WKB approximation)163

6.5.3 Application of semi-classical approximation170

6.6 The connection formulae for WKB approximation173

Chapter 7 Three-dimensional Scattering181

7.1 Asymptotic form of scattering Differential cross section181

7.2 Formal theory of scattering182

7.2.1 Lippmann-Schwinger Equation182

7.2.2 An alternative derivation of L-S equation185

7.2.3 L-S equation in coordinate representation188

7.2.4 Properties of scattering state190

7.2.5 Scattering matrix192

7.3 Pattial wave phase shift195

7.3.1 Wave function of free particle in spherical coordinate195

7.3.2 Spherical Hankel and spherical Neumann functions197

7.3.3 Partial wave expansion of scattering amplitude198

7.3.4 Three dimensional square well200

7.4 Elastic and inelastic scattering202

7.4.1 Pure elastic scattering203

7.4.2 Elastic scattering in the presence of inelastic processes203

7.4.3 Optical theorem204

7.5 Approximation methods for high energy scattering205

7.5.1 Born approximation205

7.5.2 Eikonal approximation208

7.6 Wigner-Eckart theorem213

Chapter 8 Relativistic quantum mechanics217

8.1 Klein-Gordan equation and the difficulty of negative probability217

8.2 Dirac equation219

8.3 The spin of Dirac particle221

8.4 Free particle solution of Dirac equation222

8.5 Dirac equation in electro-magnetic field Magnetic moment of electron226

Hints to Selected Exercises229

H.1 Quantum states and Physical quantities229

H.2 Time evolution of microscopic system231

H.3 Angular momentum235

H.4 Multi-particle system240

H.5 Uncertainty relation Coherent state243

H.6 One-dimensional problem Bound states and resonances246

H.7 Three-dimensional Scattering250

H.8 Relativistic quantum mechanics252

Index254