Fundamentals of Quantum Mechanics

Pdf Book Name: Fundamentals of Quantum Mechanics
Author: Ajit Kumar
Publisher: Cambridge University Press
ISBN-10, 13: 1107185580, 9781107185586
Year: 2018
Pages: 442 / 450 Pages
Language: English
File size: 3 MB
File format: PDF,EPUB

Fundamentals of Quantum Mechanics Pdf Book Description:

The book discusses fundamental concepts of quantum mechanics, including the state of a quantum mechanical system, operators, superposition principle and measurement postulate. The notion of an operator and the algebra of operators is introduced with the help of elementary concepts of mathematical analysis. The mathematical tools developed here will help resolve the difficulties encountered in classical physics while trying to explain the experimental results involving atomic spectra and other phenomena. The differential equations that arise while solving eigenvalue problems are solved rigorously, to make the text self-sufficient. The solutions are then physically interpreted and explained. The book covers modern algebraic language of quantum mechanics, wherein the fundamental concepts and methods of solutions are translated into the algebraic formalism and compared with the earlier simpler approach. The text offers solved examples and homework problems to help students in solving practical problems of physics requiring quantum mechanical treatment. Ajit Kumar is a Professor at the Department of Physics, Indian Institute of Technology, New Delhi. He is a Fellow of the Alexander von Humboldt Foundation, Bonn, Germany since 1987. A recipient of the Teaching Excellence Award from I. I. T. Delhi, he has been teaching the core subjects of theoretical physics including quantum field theory, group theory and its applications, and general theory of relativity for the past 34 years. His current research is related to the problems of nonlinear optics, solution of nonlinear Schrodinger ¨ equation in nonlinear optical media, fiber-optic solitons and their switching dynamics and electromagnetic wave propagation in metamaterials.

Before the advent of quantum mechanics, classical physics studied the universe as a system consisting of matter and radiation. Matter was supposed to be made up of tiny building blocks called particles whose motion in space and time was assumed to be governed solely by the laws of mechanics formulated by Newton. The state of a classical system at a given instant of time, t0, was completely defined by prescribing its position vector,r0, and momentum, p0. For any t > t0, this state was uniquely determined byr(t) and p(t), the solutions of Newton’s equations of motion with the initial conditions r(t0) =r0 and p(t0) = p0. Radiation, on the other hand, was assumed to be governed by the laws of electromagnetism formulated in a unified manner by James Clark Maxwell. The dynamical variables of the radiation field were the components of the electric field, E, and the magnetic field, B, at every point in space. The spatio-temporal evolution of these fields was governed by Maxwell’s equations. Unlike matter, the radiation field consisted of waves, with their characteristic properties exhibited in the phenomena of interference and diffraction. Until the end of the nineteenth century, both these theories were on firm footings. The results of the kinetic theory of gases and statistical thermodynamics made it possible to verify qualitatively and also quantitatively the basic predictions of this corpuscular theory of matter. Besides that, all the contradictions that arose between the corpuscular theory and the wave theory of radiation were overcome by Huygens and Fresnel whose wave theory of light enabled one to explain all the phenomena involving light, including geometrical optics. At this stage, it was firmly believed that all phenomena in physics could be satisfactorily explained in the general framework of matter–radiation theory. If, in some cases, the explanation was not possible, the blame was put on the mathematical difficulties involved in the solution of the problems.