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 Schrodinger'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.
Preface
Ch. 1 The wave function 1
Ch. 2 Schrodinger wave mechanics 36
Ch. 3 General principles of quantum theory 65
Ch. 4 Harmonic oscillator 106
Ch. 5 Angular momentum 130
Ch. 6 The hydrogen atom 156
Ch. 7 Spin 194
Ch. 8 Systems of identical particles 208
Ch. 9 Approximation methods 232
Ch. 10 Molecular structure 263
App. A Mathematical formulas 281
App. B Fourier series and Fourier integral 285
App. C Dirac delta function 292
App. D Hermite polynomials 296
App. E Legendre and associated Legendre polynomials 301
App. F Laguerre and associated Laguerre polynomials 310
App. G Series solutions of differential equations 318
App. H Recurrence relation for hydrogen-atom expectation values 329
App. I Matrices 331
App. J Evaluation of the two-electron interaction integral 341
Selected bibliography 344
Index
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