Solution of Certain Problems in Quantum

Intended for advanced undergraduates and graduate students in mathematics, physics, and chemistry, this work teaches problem-solving using the theory of special functions. The concise treatment presents the theory methodically and in detail to a wide variety of problems in atomic and molecular physics. The overall applicability of this method and its extension to solving these problems are discussed with attention to detail seldom found in textbooks of this level.
Starting with a brief introduction to the hypergeometric equations and their properties, a step-by-step method consisting of six distinct parts illustrates how to address typical problems in quantum physics in a simple and uniform fashion. This technique can also be applied to the solution of other problems, for which the Schrödinger equation can be reduced by some means to an equation of the hypergeometric type. Topics include the discrete spectrum eigenfunctions, linear harmonic oscillators, Kratzer molecular potential, and the rotational correction to the Morse formula. The text concludes with an Appendix that presents an original Fourier transform-based method for converting multicenter integrals to a single center.

Professor Bolotin and Professor Raudeliunas are retired from the faculty of Vilnius University in Lithuania.

Contents

Preface vii
Acknowledgments ix
1. The Hypergeometric Function 1
2. The Hypergeometric Polynomials 7
3. Discrete Spectrum Eigenfunctions 13
4. The Linear Harmonic Oscillator 17
5. The Rigid Rotor with a Free Axis 21
6. A Hydrogen-like Atom 29
7. The Kratzer Molecular Potential 33
8. Solution of the Dirac Equation for a Hydrogen-like Atom. Determination of the Radial Wave Functions and Energies for the Discrete Spectrum. 39
9. Solution of the Vibrational Problem for a Diatomic Molecule. The Morse Potential. 61
10. The Rotational Correction to the Morse Formula 69
Appendix: Transformation of Multicenter Integrals to a Single Center 79
Bibliography 85

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Solution of Certain Problems in Quantum Mechanics

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