Mathematical Physical Chemistry : Practical and Intuitive Methodology

"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 these processes 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"--Page 4 of cover Front Matter ....Pages i-xv Front Matter ....Pages 1-1 Schrödinger Equation and Its Application (Shu Hotta)....Pages 3-29 Quantum-Mechanical Harmonic Oscillator (Shu Hotta)....Pages 31-56 Hydrogen-like Atoms (Shu Hotta)....Pages 57-118 Optical Transition and Selection Rules (Shu Hotta)....Pages 119-143 Front Matter ....Pages 145-145 Maxwell’s Equations (Shu Hotta)....Pages 147-171 Reflection and Transmission of Electromagnetic Waves in Dielectric Media (Shu Hotta)....Pages 173-217 Light Quanta: Radiation and Absorption (Shu Hotta)....Pages 219-244 Introductory Green’s Functions (Shu Hotta)....Pages 245-295 Front Matter ....Pages 297-297 Vectors and Their Transformation (Shu Hotta)....Pages 299-324 Canonical Forms of Matrices (Shu Hotta)....Pages 325-385 Inner Product Space (Shu Hotta)....Pages 387-408 Hermitian Operators and Unitary Operators (Shu Hotta)....Pages 409-441 Front Matter ....Pages 443-443 Introductory Group Theory (Shu Hotta)....Pages 445-456 Symmetry Groups (Shu Hotta)....Pages 457-498 Representation Theory of Groups (Shu Hotta)....Pages 499-546 Applications of Group Theory to Physical Chemistry (Shu Hotta)....Pages 547-613 Back Matter ....Pages 615-627