Wave Mechanics Volume 5 of Pauli Lectures on Physics

by Pauli, Wolfgang

• ISBN13: 9780486414621
• ISBN10: 0486414620
• Edition: Unabridged
• Format: Paperback
• Copyright: 2000-09-18
• Publisher: Dover Publications

Summary

Peerless resource that can be used alone or as part of the complete set. Contents include wave functions of force-free particles, description of a particle in a box and in free space, particle in a field of force, more than one particle, eigenvalue problems, collision processes, matrices and operators, more.

Table of Contents

Foreword	ix
Victor F. Weisskopf
Preface by the Editor	xi
Preface by the Students	xiii
Introduction	xv
Wave Functions of Force-Free Particles	1	(22)
Association of waves with particles	1	(2)
The wave function and wave equation	3	(2)
The uncertainty principle	5	(5)
Wave packets and the mechanics of point particles. Probability density	10	(2)
Measuring arrangements. Discussion of examples	12	(7)
Classical statistics and quantum statistics	19	(4)
Description of a Particle in a Box and in Free Space	23	(15)
One particle in a box. The equation of continuity	23	(4)
Normalization in the continuum. The Dirac δ-function	27	(4)
The completeness relation. Expansion theorem	31	(2)
Initial-value problem and the fundamental solution	33	(5)
Particle in a Field of Force	38	(13)
The Hamiltonian operator	38	(2)
Hermitian operators	40	(3)
Expectation values and the classical equation of motion. Commutation relations (commutators)	43	(8)
More than One Particle	51	(4)
More than one particle	51	(4)
Eigenvalue Problems. Functions of Mathematical Physics	55	(52)
The linear harmonic oscillator. Hermite polynomials	55	(8)
Matrix calculus illustrated with the linear harmonic oscillator	63	(9)
The harmonic oscillator in a plane. Degeneracy	72	(16)
The hydrogen atom	88	(19)
Collision Processes	107	(19)
Asymptotic solution of the scattering problem	108	(2)
The scattering cross section. The Rutherford scattering formula	110	(2)
Solution of the force-free wave equation	112	(3)
Expansion of a plane wave in Legendre polynomials	115	(1)
Solution of the Schrodinger equation with an arbitrary central potential	116	(4)
The Born approximation	120	(3)
Scattering of low-energy particles	123	(3)
Approximate Methods for Solving the Wave Equation	126	(12)
Eigenvalue problem of a particle in a uniform field	126	(6)
The WKB method	132	(6)
Matrices and Operators. Perturbation Theory	138	(14)
General relationship between matrices and operators. Transformation theory	138	(5)
General formalism of perturbation theory in the matrix representation	143	(4)
Time-dependent perturbation	147	(5)
Angular Momentum and Spin	152	(13)
General commutation relations	152	(2)
Matrix elements of the angular momentum	154	(2)
Spin	156	(3)
Spinors and space rotations	159	(6)
Identical Particles with Spin	165	(12)
Symmetry classes	165	(2)
The exclusion principle	167	(2)
The helium atom	169	(4)
Collision of two identical particles: Mott's theory	173	(2)
The statistics of nuclear spins	175	(2)
Exercises	177	(14)
Fundamental solution for interval	177	(2)
Bound states and tunnel effect	179	(1)
Kronig-Penney potential	180	(1)
Spherical harmonics	180	(2)
Fundamental solution for harmonic oscillator	182	(2)
Angular momentum	184	(1)
Partial waves	185	(1)
The symmetrical top	186	(5)
Bibliography	191	(2)
Appendix. Comments by the Editor	193	(6)
Index	199