Exploring Quantum Mechanics 1st edition by Victor Galitski, Boris Karnakov, Vladimir Kogan, Victor Galitski Jr ISBN 0199232725 978-0199232727

1 Operators in quantum mechanics

1.1 Basic concepts of the theory of linear operators

1.2 Eigenfunctions, eigenvalues, mean values

1.3 The projection operators

1.4 Quantum-mechanical representations of operators and wave-functions; Unitary operators

2 One-dimensional motion

2.1 Stationary states in discrete spectrum

2.2 The Schrödinger equation in momentum space; The Green function and integral form of the Schrödinger equation

2.3 The continuous spectrum; Reflection from and transmission through potential barriers

2.4 Systems with several degrees of freedom; Particle in a periodic potential

3 Orbital angular momentum

3.1 General properties of angular momentum

3.2 Angular momentum, l = 1

3.3 Addition of angular momenta

3.4 Tensor formalism in angular momentum theory

4 Motion in a spherically-symmetric potential

4.1 Discrete spectrum states in central fields

4.2 Low-energy states

4.3 Symmetries of the Coulomb problem

4.4 Systems with axial symmetry

5 Spin

5.1 Spin s = 1/2

5.2 Spin-orbital states with spin s = 1/2; Higher spins

5.3 Spin density matrix; Angular distributions in decays

5.4 Bound states of spin-orbit-coupled particles

5.5 Coherent-state spin path-integral

6 Time-dependent quantum mechanics

6.1 The Schrödinger representation; The motion of wave packets

6.2 Time-dependent observables; Constants of motion

6.3 Time-dependent unitary transformations; The Heisenberg picture of motion

6.4 The time-dependent Green function

6.5 Quasistationary and quasi-energy states; Berry phase

7 Motion in a magnetic field

7.1 Stationary states in a magnetic field

7.2 Time-dependent quantum mechanics in a magnetic field

7.3 Magnetic field of the orbital currents and spin magnetic moment

8 Perturbation theory; Variational method; Sudden and adiabatic theory

8.1 Stationary perturbation theory (discrete spectrum)

8.2 Variational method

8.3 Stationary perturbation theory (continuous spectrum)

8.4 Non-stationary perturbation theory; Transitions in continuous spectrum

8.5 Sudden perturbations

8.6 Adiabatic approximation

9 Quasi-classical approximation; 1/N-expansion in quantum mechanics

9.1 Quasi-classical energy quantization

9.2 Quasi-classical wavefunctions, probabilities, and mean values

9.3 Penetration through potential barriers

9.4 1/N-expansion in quantum mechanics

10 Identical particles; Second quantization

10.1 Quantum statistics; Symmetry of wavefunctions

10.2 Elements of the second quantization formalism (the occupation-number representation)

10.3 The simplest systems with a large number of particles (N ≫ 1)

11 Atoms and molecules

11.1 Stationary states of one-electron and two-electron atoms

11.2 Many-electron atoms; Statistical atomic model

11.3 Principles of two-atom-molecule theory

11.4 Atoms and molecules in external fields; Interaction of atomic systems

11.5 Non-stationary phenomena in atomic systems

12 Atomic nucleus

12.1 Nuclear forces—the fundamentals; The deuteron

12.2 The shell model

12.3 Isotopic invariance

13 Particle collisions

13.1 Born approximation

13.2 Scattering theory: partial-wave analysis

13.3 Low-energy scattering; Resonant scattering

13.4 Scattering of fast particles; Eikonal approximation

13.5 Scattering of particles with spin

13.6 Analytic properties of the scattering amplitude

13.7 Scattering of composite quantum particles; Inelastic collisions

14 Quantum radiation theory

14.1 Photon emission

14.2 Photon scattering; Photon emission in collisions

15 Relativistic wave equations

15.1 The Klein–Gordon equation

15.2 The Dirac equation

16 Appendix

16.1 App.1. Integrals and integral relations

16.2 App.2. Cylinder functions

Index

Footnotes