The Elements Of Quantum Mechanics

THE ELEMENTS OF QUANTUM MECHANICS BY SAUL DUSHMAN, . PREFACE In the summer of 1932 the author was invited by Professor W. Lloyd Evans, Chairman of the Department of Chemistry, Ohio State University, Columbus, Ohio, to give a series of lectures on quantum mechanics. For the opportunity thus afforded him for study of this subject in a university atmosphere the author wishes to express his gratitude to Professor Evans. The notes prepared for these lectures were subsequently published as a serial in the Journal of Chemical Education May 1935 to August 1936, inclusive. To the editor, Dr. Otto Reinmuth, the author is indebted for many helpful suggestions with regard to method of presentation and contents. Since no reprints of the series were made available it was suggested that the contents be revised for publication in book form. As stated in the first chapter, the writers aim has been to present the subject in such a manner that its essential concepts and logic may be readily comprehended by those who have not had any intensive training in mathematics beyond calculus. For this reason there has been presented in a number of cases a great deal more detail of the mathematical development than would seem necessary to those readers who are familiar with more advanced branches of mathematics. The author lays no claim to being an expert in the field of quantum mechanics. But, like many other workers in science, he has felt a strong desire to learn something about its technic and applications. This volume may therefore be regarded in a sense as a series of notes which have served to clarify, at least to his own satisfaction, some of the difficulties which he, together with probably a considerable number of other students, has encountered in attempting to understand the subject. Should the contents of this volume prove of any assistance to others in enabling them to proceed with the study of more advanced treatises, he will feel amply rewarded for a task which has indeed been a source of intellectual pleasure. He also wishes to take this opportunity of expressing his appreciation of the sympathetic support of Dr. W. D. Coolidge, the Director of the Research Laboratory of the General Electric Company, in a task which could scarcely have been carried through without it. VI PREFACE To Dr. Frederick Seitz of this Laboratory the author is deeply grateful both for helpful discussion and clarification of difficult topics and for reading a considerable part of the galley proof. Finally the author wishes to express his indebtedness to Miss Elizabeth Gage for invaluable assistance in the typing of the manuscript and in the even more tedious task of proof-reading. SAUL DUSHMAN. RESEARCH LABORATORY GENERAL ELECTRIC COMPANY Schenectady, New York October 7, 1937. CONTENTS CHAPTER I QUANTUM PHENOMENA 1 Introductory Remarks, 1. 2 Energy States of Atomic Systems, 4. 3 Resonance Radiation, 7. 4 Photoelectric Effect, 8. 5 The Compton Effect, 10. 6 Undulatory Phenomena Associated with Corpuscles, 11. 7 Principle of Indeterminacy, 12. II THE SCHBOEDINQER EQUATION IN ONE DIMENSION 1 The Concepts of Quantum Mechanics, 19. 2 Some Fundamental Differential Equations, 20. 3 Equations for the Propagation of Wave Motion, 29. 4 Differential Equation for the Vibration of a String, 31. 5 S. Equation for One Coordinate, 36. 6 Motion of Electrons in Absence of Field of Force, 39. 7 Operator Method of Deriving the S. Equation, 42...