Quantum Mechanics by Mandl, Franz -- Read -- Imperial Library of Trantor

Index

CHAPTER 1 Basic concepts 1.1 THE STATE OF A SYSTEM 1.2 OBSERVABLES 1.3 THE SCHRÖDINGER EQUATION 1.4 MANY-PARTICLE SYSTEMS PROBLEMS 1 CHAPTER 2 Simple examples 2.1 ONE-DIMENSIONAL SQUARE-WELL POTENTIAL 2.2 POTENTIAL BARRIER 2.3 ANGULAR MOMENTUM

2.3.1 Spherical harmonics

2.4 THE STERN–GERLACH EXPERIMENT 2.5 CENTRAL POTENTIAL

2.5.1 Radial wave equation 2.5.2 The hydrogen atom

2.6 MOMENTUM EIGENSTATES

2.6.1 Box normalization 2.6.2 The continuous spectrum

*2.7 HARMONIC OSCILLATOR

PROBLEMS 2

CHAPTER 3 Several observables 3.1 COMPATIBLE OBSERVABLES

3.2 CONSTANTS OF THE MOTION 3.3 THE UNCERTAINTY PRINCIPLE

3.3.1 Proof of the uncertainty principle

PROBLEMS 3 CHAPTER 4 Symmetries 4.1 INVERSION 4.2 TRANSLATIONS 4.3 ROTATIONS 4.4 IDENTICAL PARTICLES

4.4.1 The periodic table

PROBLEMS 4 CHAPTER 5 Angular momentum I: theory 5.1 DIRAC NOTATION 5.2 THE ANGULAR MOMENTUM OF A SYSTEM

5.2.1 The basic results 5.2.2 The raising and lowering operators J±.

5.3 SPIN

5.3.1 Matrix representation of spin 5.3.2 Two-component wave functions

5.4 THE ANGULAR MOMENTUM ADDITION THEOREM 5.5 EXAMPLES OF ANGULAR MOMENTUM ADDITION

5.5.1 Two spin particles 5.5.2 Two orbital angular momenta l = 1

5.6 THE GENERAL CASE 5.7 ADDITION OF ANGULAR MOMENTUM FOR ELECTRONS *5.8 DERIVATION OF THE EIGENVALUES OF J2 AND Jz PROBLEMS 5 CHAPTER 6 Angular momentum II: applications 6.1 ATOMIC STRUCTURE

6.1.1 Spectroscopic notation 6.1 .2 Atomic multiplets 6.1.3 Spin–orbit interaction

6.2 ELECTRIC DIPOLE SELECTION RULES

6.2.1 Derivation from conservation laws 6.2.2 Hydrogenic systems 6.2.3 Many-electron atoms 6.2.4 Forbidden transitions

*6.3 BELL’S INEQUALITY PROBLEMS 6 CHAPTER 7 Bound-state perturbation theory 7.1 THE NON-DEGENERATE CASE 7.2 THE HELIUM GROUND STATE 7.3 THE DEGENERATE CASE *7.4 SPIN-ORBIT INTERACTION

7.4.1 Spin-orbit interaction in hydrogen 7.4.2 The fine structure in hydrogen 7.4.3 The fine structure in many-electron atoms

*7.5 THE ZEEMAN EFFECT

7.5.1 The weak field case: Vmag Vso 7.5.2 The strong field case: Vmag ≫ Vso 7.5.3 Derivation of Eq. (7.68)

PROBLEMS 7

CHAPTER 8 The variational method 8.1 THE GROUND STATE 8.2 SIMPLE EXAMPLES

8.2.1 The ground state of the hydrogen atom 8.2.2 The ground state of the helium atom

8.3 EXCITED STATES PROBLEMS 8 CHAPTER 9 Time dependence 9.1 INTRODUCTION 9.2 AN EXACTLY SOLUBLE TWO-STATE SYSTEM* 9.3 TIME-DEPENDENT PERTURBATION THEORY 9.4 TIME-INDEPENDENT PERTURBATIONS 9.5 EMISSION AND ABSORPTION OF RADIATION BY ATOMS

9.5.1 Spontaneous emission 9.5.2 Justifying the electric dipole approximation 9.5.3 Line width

PROBLEMS 9 CHAPTER 10 Scattering I: time-dependent approach 10.1 THE CROSS-SECTION 10.2 POTENTIAL SCATTERING

10.2.1 Density of states 10.2.2 Born approximation 10.2.3 Scattering by a screened Coulomb potential

10.3 ELECTRON-ATOM SCATTERING AT HIGH ENERGIES

PROBLEMS 10

CHAPTER 11 Scattering II: time-independent approach 11.1 THE SCATTERING AMPLITUDE 11.2 THE INTEGRAL EQUATION FOR POTENTIAL SCATTERING 11.3 BORN APPROXIMATION

★11.3.1 Validity of Born approximation

11.4 SCATTERING OF IDENTICAL PARTICLES 11.5 PARTIAL WAVES AND PHASE SHIFTS

PROBLEMS 11 CHAPTER 12 The Dirac formalism* 12.1 KETS 12.2 OPERATORS 12.3 PROBABILITY AMPLITUDES 12.4 WAVE MECHANICS REGAINED 12.5 HARMONIC OSCILLATOR 12.6 REPRESENTATIONS PROBLEMS 12 Hints and solutions to problems Bibliography Index