E-Book Overview
Quantum mechanics is the foundation of modern technology, due to its innumerable applications in physics, chemistry and even biology.
This second volume studies Schrödingers equation and its applications in the study of wells, steps and potential barriers. It examines the properties of orthonormal bases in the space of square-summable wave functions and Dirac notations in the space of states.
This book has a special focus on the notions of the linear operators, the Hermitian operators, observables, Hermitian conjugation, commutators and the representation of kets, bras and operators in the space of states. The eigenvalue equation, the characteristic equation and the evolution equation of the mean value of an observable are introduced. The book goes on to investigate the study of conservative systems through the time evolution operator and Ehrenfests theorem.
Finally, this second volume is completed by the introduction of the notions of quantum wire, quantum wells of semiconductor materials and quantum dots in the appendices.
E-Book Content
Introduction to Quantum Mechanics 2
Introduction to Quantum Mechanics 2 Wave-Corpuscle, Quantization & Schrödinger’s Equation
Ibrahima Sakho
First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK
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© ISTE Ltd 2020 The rights of Ibrahima Sakho to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2019950855 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-501-5
Contents
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
Chapter 1. Schrödinger’s Equation and its Applications . . . . . . . .
1
1.1. Physical state and physical quantity . . . . . . . . . . . 1.1.1. Dynamic state of a particle . . . . . . . . . . . . . . 1.1.2. Physical quantities associated with a particle . . . 1.2. Square-summable wave function . . . . . . . . . . . . . 1.2.1. Definition, superposition principle . . . . . . . . . . 1.2.2. Properties . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1. Definition of an operator, examples . . . . . . . . . 1.3.2. Hermitian operator . . . . . . . . . . . . . . . . . . . 1.3.3. Linear observable operator . . . . . . . . . . . . . . 1.3.4. Correspondence principle, Hamiltonian. . . . . . . 1.4. Evolution of physical systems . . . . . . . . . . . . . . . 1.4.1. Time-dependent Schrödinger equation . . . . . . . 1.4.2. Stationary Schrödinger equation . . . . . . . . . . . 1.4.3. Evolution operator . . . . . . . . . . . . . . . . . . . 1.5. Properties of Schrödinger’s equation . . . . . . . . . . . 1.5.1. Determinism in the evolution of physical systems 1.5.2. Superposition principle . . . . . . . . . . . . . . .