Principles of Quantum Mechanics: As Applied to Chemistry and Chemical Physics

by Donald D. Fitts

• ISBN13: 9780521658416
• ISBN10: 0521658411
• Format: Paperback
• Copyright: 1999-08-28
• Publisher: Cambridge University Press

Summary

This text presents a rigorous mathematical account of the principles of quantum mechanics, in particular as applied to chemistry and chemical physics. Applications are used as illustrations of the basic theory. The first two chapters serve as an introduction to quantum theory, although it is assumed that the reader has been exposed to elementary quantum mechanics as part of an undergraduate physical chemistry or atomic physics course. Following a discussion of wave motion leading to Schrödinger's wave mechanics, the postulates of quantum mechanics are presented along with essential mathematical concepts and techniques. The postulates are rigorously applied to the harmonic oscillator, angular momentum, the hydrogen atom, the variation method, perturbation theory, and nuclear motion. Modern theoretical concepts such as hermitian operators, Hilbert space, Dirac notation, and ladder operators are introduced and used throughout. This text is appropriate for beginning graduate students in chemistry, chemical physics, molecular physics and materials science.

Table of Contents

Preface	viii
The wave function	1	(35)
Wave motion	2	(6)
Wave packet	8	(7)
Dispersion of a wave packet	15	(3)
Particles and waves	18	(3)
Heisenberg uncertainty principle	21	(2)
Young's double-slit experiment	23	(3)
Stern--Gerlach experiment	26	(3)
Physical interpretation of the wave function	29	(7)
Problems	34	(2)
Schrodinger wave mechanics	36	(29)
The Schrodinger equation	36	(1)
The wave function	37	(4)
Expectation values of dynamical quantities	41	(5)
Time-independent Schrodinger equation	46	(2)
Particle in a one-dimensional box	48	(5)
Tunneling	53	(4)
Particles in three dimensions	57	(4)
Particle in a three-dimensional box	61	(4)
Problems	64	(1)
General principles of quantum theory	65	(41)
Linear operators	65	(2)
Eigenfunctions and eigenvalues	67	(2)
Hermitian operators	69	(6)
Eigenfunction expansions	75	(2)
Simultaneous eigenfunctions	77	(3)
Hilbert space and Dirac notation	80	(5)
Postulates of quantum mechanics	85	(9)
Parity operator	94	(2)
Hellmann--Feynman theorem	96	(1)
Time dependence of the expectation value	97	(2)
Heisenberg uncertainty principle	99	(7)
Problems	104	(2)
Harmonic oscillator	106	(24)
Classical treatment	106	(3)
Quantum treatment	109	(5)
Eigenfunctions	114	(7)
Matrix elements	121	(4)
Heisenberg uncertainty relation	125	(1)
Three-dimensional harmonic oscillator	125	(5)
Problems	128	(2)
Angular momentum	130	(26)
Orbital angular momentum	130	(2)
Generalized angular momentum	132	(6)
Application to orbital angular momentum	138	(10)
The rigid rotor	148	(3)
Magnetic moment	151	(5)
Problems	155	(1)
The hydrogen atom	156	(38)
Two-particle problem	157	(3)
The hydrogen-like atom	160	(1)
The radial equation	161	(14)
Atomic orbitals	175	(12)
Spectra	187	(7)
Problems	192	(2)
Spin	194	(1)
Electron spin	194	(2)
Spin angular momentum	196	(2)
Spin one-half	198	(3)
Spin--orbit interaction	201
Problems