Contents
1.2 The usual (classical) mechanics
1.3 The process of observation
Chapter 2 Wave-particle Duality
2.2 Young’s two-slit experiment
2.6 Wave-particle nature of electromagnetic radiations
2.7 Electron/neutron diffraction
2.8 Davisson and Germer electron diffraction experiment
2.9 Wave-particle nature of matter
2.10 What is the real nature of matter and radiations?
Chapter 3 Wave Packets and Uncertainty Principle
3.3 Phase velocity and group velocity
3.5 Measurement and uncertainty principle
3.6 Uncertainty principle: Thought experiments
Chapter 4 Operators, Eigenstates, Eigenvalues and Schrodinger Equation
4.3 Physical interpretation of wave function ψ(r, t)
4.4 Schrodinger equation for a free particle
4.5 Schrodinger equation for a free wave packet
4.6 Schrodinger equation for a particle in a potential
4.7 Expectation value and operators
4.8 Probability current density: Equation of continuity
4.9 Gaussian wave packet and its spread with time
4.10 Wave function in momentum space
4.12 The uncertainty relations (revisited)
4.13 The (resulting) quantum logic
Chapter 5 One-dimensional Problems
5.2 Time-independent schrodinger equation and stationary states
5.3 Some characteristics of wave functions
5.4 Particle in a one-dimensional potential box
5.5 Potential box with periodic boundary conditions
5.7 Rectangular potential barrier
5.8 Potential well of finite depth
Chapter 6 The Linear Harmonic Oscillator
6.2 Classical harmonic oscillator
6.3 Quantum harmonic oscillator
6.4 The Normalized Wave Functions
Chapter 7 The Linear Vector Space
7.2 Some characteristics of eigenstates of Hermitian operators
7.3 Dirac bra and ket notations
7.4 More about bra, ket vectors and linear vector space
7.5 Matrix representation of state vectors and operators
7.6 Some special matrices/operators
7.7 Change of basis: Unitary transformation
7.8 Tensor product or direct product of vector spaces
Chapter 8 Linear Harmonic Oscillator—Revisited
8.2 The creation and annihilation operators
8.4 Matrix representation of various operators
8.5 Expectation values of various operators
8.7 Time evolution of the coherent state and its comparison with classical oscillator
8.8 The Schrodinger and Heisenberg pictures
9.2 Orbital angular momentum operator
9.4 Angular momentum operator in spherical polar coordinates
9.5 The eigenvalues and eigenfunctons of 
and 
9.6 Measurement of angular momentum components and the uncertainty relations
9.7 Orbital angular momentum and spatial rotation
Chapter 10 Three-dimensional Systems
10.2 A particle in a cubic potential box
10.3 Cubic box with periodic boundary conditions
10.4 Density of states of free particles (free electron gas in metals)
10.5 Spherically symmetric potentials
10.6 The free particle in spherical polar coordinates
10.7 Schrodinger equation for a two-body system
Chapter 11 Angular Momentum—Revisited
11.2 Raising and lowering operators (the ladder operators)
11.5 Matrix representation of angular momentum operator corresponding to j = 1
11.6 Matrix representation of angular momentum operator corresponding to j = ½
12.2 Orbital angular momentum and magnetic moment
12.3 The electron spin: Spin operators and spin eigenstates
12.4 Total wave function of an electron
12.5 The Stern–Gerlach experiment
12.6 Spin and rotation (spinor transformation)
12.7 A magnetic moment in a uniform magnetic field: The Larmor precession
Chapter 13 Addition of Angular Momenta
13.2 Addition of two angular momenta
13.3 Recursion relations for the C–G coefficients
13.5 Addition of two spin ½ angular momenta
13.6 Addition of j = 1 and j = ½ angular momenta
Chapter 14 WKB Approximation and Electron Tunnelling
14.2 The essential idea of WKB method
14.3 Development of WKB approximation
14.4 Validity of WKB approximation
14.6 Application of WKB technique to barrier penetration
14.7 Cold emission of electrons from metals
Chapter 15 Time-independent Perturbation Theory
15.2 Non-degenerate perturbation theory
15.3 Harmonic oscillator subject to perturbing potential
15.4 Degenerate perturbation theory
15.6 The fine structure of hydrogen
Chapter 16 Time-dependent Perturbation Theory
16.2 Time development of states and transition probability
16.4 The adiabatic approximation
Chapter 17 Semi-classical Theory of Radiations
17.2 Interaction of one-electron atom with electromagnetic field
17.3 Harmonic perturbation theory
17.4 Spontaneous emission: Einstein A and B coefficients
17.5 Selection rules for electric dipole transitions
Chapter 18 Theory of Scattering
18.2 Scattering experiments and scattering cross-section
18.3 Classical theory of scattering: Rutherford scattering
18.4 Quantum theory of scattering
18.5 Solution of Schrodinger equation for scattering problem: Green’s function
18.7 Method of partial waves and phase shifts
Chapter 19 Theory of Measurement in Quantum Mechanics
19.2 Process of measurement: A simple treatment
19.3 Measurement of spin of an atom
19.5 The hidden variables and Bell’s theorem
19.6 Time–evolution of a system: Quantum zeno paradox
Chapter 20 Introduction to Quantum Computing
Appendix A Early Quantum Mechanics
A.1 Planck’s formula of black body radiations
A.2 Atomic spectra and Bohr’s model of hydrogen atom
A.3 Bohr’s correspondence principle
A.4 The Franck–Hertz experiment
Appendix B Some Supplementary Topics
Appendix C Some Mathematical Relations
C.2 Some trigonometric relations
D.1 Table of fundamental physical constants
D.2 Table of conversion factors between units used to express magnitude of energy
D.3 Table of spectrum of electromagnetic radiations