Mathematical Physical Chemistry

Chapter 1. Schrödinger Equation and Its Application.- Chapter 2. Quantum-Mechanical Harmonic Oscillator.- Chapter 3. Hydrogen-Like Atoms.- Chapter 4. Optical Transition and Selection Rules.- Chapter 5. Approximation Methods of Quantum Mechanics.- Chapter 6. Theory of Analytic Functions.- Chapter 7. Maxwell’s Equations.- Chapter 8. Reflection and Transmission of Electromagnetic Waves in Dielectric Media.- Chapter 9. Light Quanta: Radiation and Absorption.- Chapter 10. Introductory Green’s Functions.- Chapter 11. Vectors and Their Transformation.- Chapter 12. Canonical Forms of Matrices.- Chapter 13. Inner Product Space.- Chapter 14. Hermitian Operators and Unitary Operators.- Chapter 15. Exponential Functions of Matrices.- Chapter 16. Introductory Group Theory.- Chapter 17. Symmetry Groups.- Chapter 18. Representation Theory of Groups.- Chapter 19. Applications of Group Theory to Physical Chemistry.- Chapter 20.Theory of Continuous Groups.- Chapter 21. The Dirac Equation.- Chapter22. Quantization of Fields.- Chapter 23. Interaction between Fields.- Chapter 24. Basic Formalism.- Chapter 25. Advanced Topics of Lie Algebra.

“This book is a standard textbook on quantum mechanics intended for graduate and undergraduate students, mainly in chemistry, ‘who wish to study mathematical physics’ … . this is a standard tutorial book for the chemistry-oriented students, very detailed and very transparent.”

This book introduces basic concepts of mathematical physics to chemists. Many textbooks and monographs of mathematical physics may appear daunting to them. Unlike other, related books, however, this one contains a practical selection of material, particularly for graduate and undergraduate students majoring in chemistry. The book first describes quantum mechanics and electromagnetism, with the relation between the two being emphasized. Although quantum mechanics covers a broad field in modern physics, the author focuses on a hydrogen(like) atom and a harmonic oscillator with regard to the operator method. This approach helps chemists understand the basic concepts of quantum mechanics aided by their intuitive understanding without abstract argument, as chemists tend to think of natural phenomena and other factors intuitively rather than only logically. The study of light propagation, reflection, and transmission in dielectric media is of fundamental importance. This book explains theseprocesses on the basis of Maxwell equations. The latter half of the volume deals with mathematical physics in terms of vectors and their transformation in a vector space. Finally, as an example of chemical applications, quantum chemical treatment of methane is introduced, including a basic but essential explanation of Green functions and group theory. Methodology developed by the author will also prove to be useful to physicists. 

Contains a judicious selection of material to help chemists understand the basic concepts of quantum mechanics and electromagnetism without abstract argument Shows how an operator method fits well with chemists' intuitive understanding Includes methodology that the author developed that will be useful to physicists