Mathematics for Quantum Mechanics An Introductory Survey of Operators, Eigenvalues, and Linear Vector Spaces

by Jackson, John David

• ISBN13: 9780486453088
• ISBN10: 0486453081
• Format: Paperback
• Copyright: 2006-10-06
• Publisher: Dover Publications

Summary

This concise text for advanced undergraduates and graduate students covers eigenvalue problems in classical physics, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. It emphasizes the unity of a variety of techniques and is enduringly relevant to many physical systems. 1962 edition.

Author Biography

John David Jackson is Professor Emeritus at the University of California, Berkeley.

Table of Contents

Editors' Foreword	v
Preface	vii
Introductory Remarks	1	(3)
References	2	(2)
Eigenvalue Problems in Classical Physics	4	(18)
Vibrating string	4	(2)
Vibrating circular membrane	6	(4)
Small oscillations of a mechanical system	10	(5)
Rotation of axes and orthogonal transformations	15	(3)
Euler's theorem and principal-axes transformations as eigenvalue problems	18	(4)
Orthogonal Functions and Expansions	22	(19)
Fourier series	22	(3)
Expansion in orthonormal functions	25	(3)
Dirac delta function and closure relation	28	(3)
Bessel functions as an orthonormal set on the interval (0,1)	31	(2)
Schmidt orthogonalization method	33	(2)
Legendre polynomials	35	(1)
Other orthogonal polynomials	36	(1)
Fourier integrals	37	(4)
Sturm-Liouville Theory and Linear Operators on Functions	41	(7)
Sturm-Liouville eigenvalue problem	41	(2)
Linear operators on functions	43	(2)
Eigenvalue problem for a linear Hermitean operator	45	(1)
Further properties of operators	46	(2)
Linear Vector Spaces	48	(31)
State vectors and representatives	48	(1)
Complex vectors in a n-dimensional Euclidean space	49	(2)
Basis and base vectors	51	(2)
Change of basis	53	(3)
Linear operators and their matrix representation	56	(3)
Further definitions and properties of linear operators	59	(4)
Unitary operators and equations of motion	63	(3)
Eigenvectors, eigenvalues, and spectral representation	66	(2)
Determination of eigenvalues and eigenvectors	68	(4)
Transition to Hilbert space; Dirac notation	72	(3)
State vectors and wave functions	75	(4)
Appendix A: Bessel (Cylinder) Functions	79	(9)
Appendix B: Legendre Functions and Spherical Harmonics	88