- 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
Principles of Quantum Mechanics
Ishwar Singh Tyagi
Physics Department
Indian Institute of Technology Roorkee
Roorkee, Uttrakhand
Delhi • Chennai
-
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.