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College Physics

Comments on Zeng Jinyan's textbooks of quantum mechanics

Guan Hong

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Some basic concepts stated in Zeng Jinyan's textbooks of quantum mechanics are commented.The questions involved are: concept of free particle,meaning of superposition principle,reason of assuming Hermitian operator,interference of photons,identity principle and symmetrical postulate

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The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."
This book is a comprehensive text in the field of quantum mechanics, covering fundamental concepts including the state of a quantum mechanical system, operators, superposition principle and measurement postulate. The notion of an operator and the algebra of operators are introduced with the help of elementary concepts of mathematical analysis. Mathematical tools developed will help readers in understanding 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 text offers solved examples, analogous and homework problems to help students in solving practical problems of physics requiring quantum mechanical treatment.
Abstract Chapter 9 begins laying a foundation for quantum statistical mechanics with a discussion of relevant topics in quantum mechanics. The fundamental postulates of quantum mechanics are reviewed, beginning with the definition of a quantum state and the introduction of the concept of a state vector in a Hilbert space. The representation of observables as Hermitian operators on Hilbert space vectors is described; it is shown that the eigenvalues of Hermitian operators are real and, therefore, constitute possible outcomes of measurements made on these observables. The notions compatible and non-compatible observables and implication for the measurement problem are presented. The time-dependent Schrödinger equation is introduced as generating the time-evolution of the state vector, and it is shown how to cast the Schrödinger equation into a coordinate basis to yield the wave equation of quantum mechanics. Coordinate and momentum bases and their properties are desribed. Several analytically solvable quantum systems are presented as illustrative examples. The chapter concludes with a discussion of spin and the treatment identical particles
Covers the basic principles and theories of engineering physics and offers a balance between theoretical concepts and their applications. It is designed as a textbook for an introductory course in engineering physics. Beginning with a comprehensive discussion on oscillations and waves with applications in the field of mechanical and electrical engineering, it goes on to explain the basic concepts such as Huygen's principle, Fresnel's biprism, Fraunhofer diffraction and polarization. Emphasis has been given to an understanding of the basic concepts and their applications to a number of engineering problems. Each topic has been discussed in detail, both conceptually and mathematically. Pedagogical features including solved problems, unsolved exercised and multiple choice questions are interspersed throughout the book. This will help undergraduate students of engineering acquire skills for solving difficult problems in quantum mechanics, electromagnetism, nanoscience, energy systems and other engineering disciplines.