Quantum Mechanics: Theory and Applications

An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.

A comprehensive account of Quantum Mechanics with an excellent balance between theory and applications

I: Mathematical Preliminaries.- 1: The Dirac Delta Function.- 2: Fourier Transforms.- II: Basic Quantum Mechanics.- 3: Particles and Waves and the Uncertainty Principle.- 4: Time Dependent Schrödinger Equation.- 5: Propagation of Wave Packets and Concept of Group Velocity.- 6: Bound State Solutions of the Schrödinger Equation.- 7: Linear Harmonic Oscillator: I Solution of the Schrödinger Equation and Relationship with the Classical Oscillator.- 8: One-Dimensional Barrier Transmission Problems.- 9: Angular Momentum I The Spherical Harmonics.- 10: Spherically Symmetric Potentials Hydrogen Atom Problem, Rotation Vibration Spectra, Three-Dimensional Oscillator.- 11: Dirac's Bra and Ket Algebra.- 12: Linear Harmonic Oscillator II Solutions Using Bra and Ket Algebra.- 13: Angular Momentum II Using Bra and Ket Algebra.- 14: Experiments with Spin Half Particles The Stern-Gerlach Experiment, Larmor Precession and Magnetic Resonance.- 15: Angular momentum III Eigenfunctions Using Operator Algebra.- 16: The Double Well Potential and the Krönig-Penney Model.- 17: The JWKB Approximation.- 18: Addition of Angular Momenta: The Clebsch-Gordan Coefficients.- 19: Time Independent Perturbation Theory.- 20: Effects of Magnetic Field.- 21: The Variational Method.- 22: The Helium Atom and the Exclusion Principle.- 23: Some Select Topics.- 24: Elementary Theory of Scattering.- 25: Time Dependent Perturbation Theory.- 26: The Semi-Classical Theory of Radiation and the Einstein Coefficients.- 27: The Quantum Theory of Radiation and Its Interaction with Matter.- 28: Relativistic Theory.- Appendices.