Students can explore quantum mechanics with a concept map that uses only the most elementary solutions to Schrödinger's equation. The content has been slightly modified from the traditional introduction to the subject because the issue of interpretation is postponed until Parseval's theorem is reached and used to postulate two fundamental equations of probability, simultaneously. A set of canonical but approximate equations can describe wavepacket motion for most linear waves. If restricted to certain special cases, these equations of wavepacket motion are easily derived and can serve as a temporary substitute for Ehrenfest's theorem. A number of exercises can be incorporated into this maze of quantum mechanics.
Students can explore quantum mechanics with a concept map that uses only the most elementary solutions to Schrödinger's equation. The content has been slightly modified from the traditional introduction to the subject because the issue of interpretation is postponed until Parseval's theorem is reached and used to postulate two fundamental equations of probability, simultaneously. A set of canonical but approximate equations can describe wavepacket motion for most linear waves. If restricted to certain special cases, these equations of wavepacket motion are easily derived and can serve as a temporary substitute for Ehrenfest's theorem. A number of exercises can be incorporated into this maze of quantum mechanics.
Abstract A discussion of the physical meaning of the Schrödinger wave equation can not only constitute an exciting introduction to some of the more abstract ideas of quantum mechanics, but serves more generally as a useful demonstration of the application of mathematics to modern physics. This frontline uses physical concepts and mathematical techniques that would be accessible to a sufficiently interested secondary school student, in order to derive the simplest, one-dimensional case of the time-independent Schrödinger equation: the derivation relies only upon aspects of Newtonian/wave mechanics, quantum theory, complex numbers and calculus that would be covered in an advanced secondary school syllabus.
Many physics textbooks take a traditional approach to the demonstration of mathematical relationships and derivations, presenting them in linear order. However, many physical derivations follow a tree-shaped structure with interconnected steps running in parallel, where numerous individual equations are manipulated and combined to reach a final result. Thus, conventional presentation often leads to derivations being spread over several book pages and linked by formula numbering. This title takes a novel and intuitive approach to introductory quantum mechanics by utilising concept maps to address non-linear structures in key mathematical relationships. Concept maps are structures in a form similar to flowcharts where derivations, concepts, and relations are visualised on one page, supported by concise accompanying text on the opposite page. Perfect as a supporting and guiding tool for undergraduates, this book is designed to aid in the understanding and memorisation of key derivations and mathematical concepts in quantum mechanics.
Many physics textbooks take a traditional approach to the demonstration of mathematical relationships and derivations, presenting them in linear order. However, many physical derivations follow a tree-shaped structure with interconnected steps running in parallel, where numerous individual equations are manipulated and combined to reach a final result. Thus, conventional presentation often leads to derivations being spread over several book pages and linked by formula numbering. This title takes a novel and intuitive approach to introductory quantum mechanics by utilising concept maps to address non-linear structures in key mathematical relationships. Concept maps are structures in a form similar to flowcharts where derivations, concepts, and relations are visualised on one page, supported by concise accompanying text on the opposite page. Perfect as a supporting and guiding tool for undergraduates, this book is designed to aid in the understanding and memorisation of key derivations and mathematical concepts in quantum mechanics.
Main features:i) A different approach for teaching Quantum Mechanics encompassing old quantum mechanics, matrix mechanics and wave mechanics in a historical perspective which helps to consolidate most important concepts of Quantum Mechanics;ii) Original information from the most important papers of Quantum Mechanics;iii) Derivation of all important equations of Quantum Mechanics, for example, Heisenberg’s uncertainty principle, de Broglie’s wave-particle duality, Schrödinger’s wave equation, etc., showing their interrelations through Dirac’s equations and other applications of matrix and wave mechanics;iv) Comprehensive mathematical support for the understanding of Quantum Mechanics; derivation of all equations make reading easier;v) The illustrations of the book cover examples, exercises and do-it-yourself activities;vi) Fundamentals of Fortran and numerical calculation along with the source codes for numerical solutions of several mathematical and quantum problems. All source codes are in the author’s site: (https://www.fortrancodes.com/);vii) Chapters devoted to linear algebra and differential equations applied to quantum mechanics and their numerical solutions;viii) Complete solution for the one-electron and two-electron problems using Schrödinger’s time independent equation along with their source codes.
The book is designed to serve as an `upper-level one-semester course in Quantum mechanics for students majoring in physics or related topics'. To that purpose the author has organised the contents into roughly six parts, giving first a historical introduction into quanta and matter waves, then the solution of the Schrödinger equations in one, and subsequently in three dimensions; in a fourth part spin and the concept of identical particles are explained, whilst in the next the approximation (perturbation) methods and their application to atomic systems and the creation and transfer of radiations. Finally there are two chapters on molecular and solid state physics. Each chapter is accompanied by a selection of appropriate problems. Appendix, index plus diskette are provided. As the author states, the topics and examples were taken from his other (successful) book, Introduction to Modern Physics . It appears to the reviewer that the present account may indeed serve as a first introduction into the elementary aspects of quantum mechanics, with particular emphasis on explaining the basic concepts (like spin, statistics, even the Einstein-Podolsky-Rosen paradox). Addressed are the slightly advanced students of science. The language is clear, the formal apparatus does not overwhelm the reader, and the figures have been carefully selected and drawn. We do recommend the book for the purpose envisaged. It raises the appetite for a more systematic and extended study of the subject.
Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.