Introduction To Quantum Mechanics
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| Introduction To Quantum Mechanics |
In writing this book we have attempted to produce a textbook of practical quantum mechanics for the chemist, the experimental physicist, and the beginning student of theoretical physics. The book is not intended to provide a critical discussion of quantum mechanics, nor even to presen^ia thorough survey of the subject.
The effort has been made to provide for the reader a means of equipping himself with a practical grasp of this subject so that he can apply quantum mechanics to most of the chemical and physical problems which may confront him.
The book is particularly designed for study by men without extensive previous experience with advanced mathematics, such as chemists interested in the subject because of its chemical applications. We have assumed on the part of the reader, in addition to elementary mathematics through calculus, only some knowledge of complex quantities, ordinary differential equations, and the technique of partial differentiation. It may be desirable that a book is written for the reader not adept at mathematics be richer in equations than one intended for the mathematician; for the mathematician can follow a sketchy derivation with ease, whereas if the less adept reader is to be led safely through the usually straightforward but sometimes rather complicated derivations of quantum mechanics a firm guiding hand must be kept on him.
Quantum mechanics is essentially mathematical in character, and an understanding of the subject without a thorough knowledge of the mathematical methods involved and the results of their application cannot be obtained.
The student not thoroughly trained in the theory of partial differential equations and orthogonal functions must learn something of these subjects as he studies quantum mechanics. In order that he may do so, and that he may follow the discussions given without danger of being deflected from the course of the argument by the inability to carry through some minor step, we have avoided the temptation to condense the various discussions into shorter and perhaps more elegant forms.
After introductory chapters on classical mechanics and the old quantum theory, we have introduced the Schroding^r wave equation and its physical interpretation on a postulatory basis, and have then given in great detail the solution of the wave equation for important systems (harmonic oscillator, hydrogen atom) and the discussion of the wave functions and their properties, omitting none of the mathematical steps except the most similarly detailed treatment has been given in the discussion di pert in 1 option Shruor^, the variation method, the structure of simple molecules, and, in general, an unimportant section of the book.
In order to limit the size of the book, we have omitted from discussion such advanced topics as transformation theory and general quantum mechanics (aside from a brief mention in the last chapter), the Dirac theory of the electron, quantization of the electromagnetic field, etc. We have also omitted several subjects which are ordinarily considered as part of elementary quantum mechanics, but which are of minor importance to the chemist, such as the Zeeman effect and magnetic interactions in general, the dispersion of light and allied phenomena, and most of the theory of aperiodic processes.
The authors are severally indebted to Professor A. Sommerfeld and Professors E. U. Condon and H. P. Robertson for their own introduction to quantum mechanics.
Some contents:
CHAPTER II
SURVEY OF CLASSICAL MECHANICS
1. Newton's Equations of Motion in the Lagntngian Form ..... 2
la. The Three-dimensional Isotropic Harmonic Oscillator. . 4
Ib. Generalized Coordinates .......... \. A . . . . 6
Ic. The Invariance of the Equations of Motion in the Lagraibgian Form .................... 7
Id. An Example: The Isotropic Harmonic Oscillator in Polar Coordinates .................... 9
le. The Conservation of Angular Momentum . . . 11
2. The Equations of Motion in the Hamiltonian Form ...... 14
2a. Generalized Momenta ................. 14
2b The Hamiltonian Function and Equations ....... 16
2c. The Hamiltonian Function and the Energy ...... 16
2d. A General Example ............... 17
3. The Emission and Absorption of Radiation. . ...... 21
4. Summary of Chapter I ............ ....... 23
CHAPTER II
THE OLD QUANTUM THEORY
THE OLD QUANTUM THEORY
5. The Origin of the Old Quantum Theory ........... 25
5a. The Postulates of Bohr ................ 26
56. The Wilson-Sommerfeld Rules of Quantization ...... 28
5c. Selection Rules. The Correspondence Principle ..... 29
6. The Quantization of Simple Systems .............. 30
6a. The Harmonic Oscillator. The Degenerate States ...... 30
6b. The Rigid Rotator .................. 31
6c. The Oscillating and Rotating Diatomic Molecule ..... 32
6d. The Particle in a Box ................. 33
6e. Diffraction by a Crystal Lattice ........... 34
7. The Hydrogen Atom .................... 36
7a. Solution of the Equations of Motion .......... 36
7b. Application of the Quantum Rules. The Energy Levels . . 39
7c. Description of the Orbits ............... 43
7e. Spatial Quantization ................. 45
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