- Cover
- Title Page
- Contents
- About the Author
- Dedication
- Foreword
- Preface
- Chapter 1: Introduction
- Chapter 2: Wave-particle Duality
- 2.1 Introduction
- 2.2 Young’s two-slit experiment
- 2.3 Bragg’s x-ray diffraction
- 2.4 Photoelectric effect
- 2.5 Compton effect
- 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?
- Exercises
- Solutions
- References
- Chapter 3: Wave Packets and Uncertainty Principle
- Chapter 4: Operators, Eigenstates, Eigenvalues and Schrodinger Equation
- 4.1 Introduction
- 4.2 Measurement process as operator operating on the state function/wave function of a particle having definite linear momentum
- 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
- 4.11 The Ehrenfest theorem
- 4.12 The uncertainty relations (revisited)
- 4.13 The (resulting) quantum logic
- Exercises
- Solutions
- References
- Chapter 5: One-dimensional Problems
- 5.1 Introduction
- 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
- 5.6 The potential step
- 5.7 Rectangular potential barrier
- 5.8 Potential well of finite depth
- 5.9 Kronig–Penney model
- Exercises
- Solutions
- References
- Chapter 6: The Linear Harmonic Oscillator
- Chapter 7: The Linear Vector Space
- 7.1 Introduction
- 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
- 7.9 Outer product operators
- Exercises
- Solutions
- References
- Chapter 8: Linear Harmonic Oscillator—Revisited
- 8.1 Introduction
- 8.2 The creation and annihilation operators
- 8.3 Energy eigenstates
- 8.4 Matrix representation of various operators
- 8.5 Expectation values of various operators
- 8.6 The coherent states
- 8.7 Time evolution of the coherent state and its comparison with classical oscillator
- 8.8 The Schrodinger and Heisenberg pictures
- Exercises
- Solutions
- References
- Chapter 9: Angular Momentum
- 9.1 Introduction
- 9.2 Orbital angular momentum operator
- 9.3 Commutation relations
- 9.4 Angular momentum operator in spherical polar coordinates
- 9.5 The eigenvalues and eigenfunctons of L2 and Lz
- 9.6 Measurement of angular momentum components and the uncertainty relations
- 9.7 Orbital angular momentum and spatial rotation
- Exercises
- Solutions
- References
- Chapter 10: Three-dimensional Systems
- 10.1 Introduction
- 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
- 10.8 The hydrogenic atom
- Exercises
- Solutions
- References
- Chapter 11: Angular Momentum—Revisited
- 11.1 Introduction
- 11.2 Raising and lowering operators (the ladder operators)
- 11.3 Eigenvalues and eigenstates of orbital angular momentum operators: Second construction of spherical harmonics
- 11.4 The constants C+ and C–
- 11.5 Matrix representation of angular momentum operator corresponding to j = 1
- 11.6 Matrix representation of angular momentum operator corresponding to j = 1/2
- Exercises
- Solutions
- References
- Chapter 12: The Spin
- 12.1 Introduction
- 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
- 12.8 Electron spin resonance
- Exercises
- Solutions
- References
- Chapter 13: Addition of Angular Momenta
- Chapter 14: WKB Approximation and Electron Tunnelling
- 14.1 Introduction
- 14.2 The essential idea of WKB method
- 14.3 Development of WKB approximation
- 14.4 Validity of WKB approximation
- 14.5 The connection formulae
- 14.6 Application of WKB technique to barrier penetration
- 14.7 Cold emission of electrons from metals
- 14.8 Alpha-decay of nuclei
- Exercises
- Solutions
- References
- Chapter 15: Time-independent Perturbation Theory
- Chapter 16: Time-dependent Perturbation Theory
- Chapter 17: Semi-classical Theory of Radiations
- Chapter 18: Theory of Scattering
- 18.1 Introduction
- 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
- 18.6 The Born approximation
- 18.7 Method of partial waves and phase shifts
- Exercises
- Solutions
- References
- Chapter 19: Theory of Measurement in Quantum Mechanics
- Chapter 20: Introduction to Quantum Computing
- Appendices
- Copyright
Appendix D
Various Tables
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
D.4 Range of Radiations
|
Radiations |
Range in Frequency (Hz) |
Range in Wavelength |
|---|---|---|
|
Gamma rays |
3.0 × 1021 – 3.0 × 1018 |
.001 – 1.00Å |
|
X-rays |
3.0 × 1019 – 3.0 × 1016 |
0.1 – 100Å |
|
Ultraviolet |
3.0 × 1017 – 7.5 × 1014 |
10 – 4000Å |
|
Visible |
7.5 × 1014 – 4.0 × 1014 |
4000 – 7500Å |
|
Infrared |
4.0 × 1014 – 2.0 × 1013 |
7500Å – 15 µm |
|
Far infrared |
2.0 × 1013 – 3.0 × 1010 |
15 µm – 1 mm |
|
Microwave |
3.0 × 1012 – 3.0 × 108 |
0.1 mm – 1 m |
|
Radiowaves |
3.0 × 109 – 3.0 × 103 |
10 cm – 100 km |
D.5 Symbols and Values of Pre-factors
|
Pre-factor |
Symbol |
Value |
|---|---|---|
|
femto |
f |
10–15 |
|
pico |
P |
10–12 |
|
nano |
n |
10–9 |
|
micro | µ |
10–6 |
|
mili |
m |
10–3 |
|
kilo |
k |
103 |
|
Mega, million |
M |
106 |
|
Giga |
G |
109 |
|
Tera |
T |
1012 |
D.6 The Greek Alphabets
-
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