Quantum Mechanics: Theory and Applications by Ajoy Ghatak PDF - A Comprehensive Review
Quantum mechanics is one of the most fascinating and challenging subjects in physics. It describes the behavior of matter and energy at the smallest scales, where the classical laws of Newton and Maxwell fail. Quantum mechanics reveals the fundamental nature of reality, such as the wave-particle duality, the uncertainty principle, and the superposition principle. It also provides the foundation for many modern technologies, such as lasers, semiconductors, and nuclear power.
However, quantum mechanics is not easy to learn or master. It requires a lot of mathematical tools and concepts, such as complex numbers, linear algebra, differential equations, and operators. It also involves many abstract and counter-intuitive phenomena, such as entanglement, tunneling, and quantum interference. Therefore, a good textbook is essential for anyone who wants to study quantum mechanics.
One of the best textbooks on quantum mechanics is Quantum Mechanics: Theory and Applications by Ajoy Ghatak and S. Lokanathan. This book covers all the basic topics in quantum mechanics, such as the Schrödinger equation, the harmonic oscillator, the hydrogen atom, angular momentum, perturbation theory, scattering theory, and relativistic theory. It also includes many advanced topics, such as the Dirac equation, the quantum theory of radiation, the semi-classical theory of radiation, and the quantum theory of solids.
The book is written in a clear and rigorous style, with many examples and exercises to illustrate the concepts and methods. The book also derives many results from first principles, making it suitable for self-study. The book also emphasizes the applications of quantum mechanics in various fields of physics, such as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum optics. The book also provides a historical perspective on the development of quantum mechanics and its impact on science and society.
The book is divided into 24 chapters and 7 appendices. The first chapter introduces the basic concepts of quantum mechanics, such as wave-particle duality and uncertainty principle. The second chapter reviews some mathematical tools needed for quantum mechanics, such as Fourier transforms and Dirac delta functions. The third chapter discusses the time-dependent Schrödinger equation and its solutions for free particles and wave packets. The fourth chapter deals with bound state solutions of the Schrödinger equation for various potentials, such as square wells and harmonic oscillators. The fifth chapter presents two different methods for solving the harmonic oscillator problem: operator algebra and Dirac bra-ket notation. The sixth chapter analyzes one-dimensional barrier transmission problems, such as tunneling and reflection.
The seventh chapter introduces the concept of angular momentum and its eigenfunctions, the spherical harmonics. The eighth chapter applies the angular momentum theory to the spherically symmetric potentials, such as the hydrogen atom problem. The ninth chapter explains how to add two angular momenta and obtain the Clebsch-Gordan coefficients. The tenth chapter discusses the time-independent perturbation theory and its applications, such as the Stark effect and the Zeeman effect. The eleventh chapter studies the effects of magnetic field on quantum systems, such as the diamagnetism and paramagnetism of atoms.
The twelfth chapter presents the variational method and its applications, such as the helium atom and the hydrogen molecule. The thirteenth chapter explores the helium atom and the exclusion principle, which leads to the concept of spin and the Pauli matrices. The fourteenth chapter covers some select topics, such as the double well potential, the Kronig-Penney model, and the quantum well structures. The fifteenth chapter develops the elementary theory of scattering and its applications, such as the Rutherford scattering and the Born approximation. The sixteenth chapter deals with the time-dependent perturbation theory and its applications, such as the Fermi's golden rule and the transition probabilities.
The seventeenth chapter introduces the Dirac's bra and ket algebra and its applications, such as the projection operators and the completeness relation. The eighteenth chapter revisits the linear harmonic oscillator problem using the bra and ket algebra and shows how to study the evolution of the coherent state. The nineteenth chapter revisits the angular momentum problem using the bra and ket algebra and shows how to construct the ladder operators and the matrix representations. The twentieth chapter describes some experiments with spin half particles, such as the Stern-Gerlach experiment, the Larmor precession, and the magnetic resonance.
The twenty-first chapter revisits the angular momentum problem using the operator algebra and shows how to obtain the Wigner-Eckart theorem and the Racah coefficients. The twenty-second chapter discusses some topics related to the double well potential and the Kronig-Penney model, such as the tunneling effect, the band structure, and the Bloch theorem. The twenty-third chapter explains the JWKB approximation and its applications, such as the alpha decay and the quantum mechanical phase. The twenty-fourth chapter covers some topics related to the semi-classical theory of radiation and the quantum theory of radiation, such as the Einstein coefficients, the Planck's law, and the interaction of radiation with matter.
The book also includes seven appendices that cover some topics in more detail, such as the Dirac delta function, the Fourier transforms, the Legendre polynomials, the Laguerre polynomials, the Hermite polynomials, the spherical Bessel functions, and the gamma function. The book also provides a list of references for further reading and a comprehensive index for easy access to the topics.
The book is suitable for undergraduate and graduate students who want to learn quantum mechanics in a rigorous and comprehensive way. It is also useful for researchers and professionals who want to refresh their knowledge or explore new applications of quantum mechanics. The book is written by Ajoy Ghatak and S. Lokanathan, who are both eminent physicists and educators with decades of experience in teaching and research. The book is available in both print and electronic formats from Springer Science & Business Media. d282676c82