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Simple Theorems, Proofs, and Derivations in Quantum Chemistry
A self-containing advanced textbook offering full, step-by-step derivations of different basic results of quantum chemistry, using only simple methods of "elementary" quantum mechanics. There are neither second quantization, nor diagrams, nor density matrices and practically no group theory in the book; the bracket formalism used occasionally is introduced in an appendix. The book contains several classical results that must be known to professionals within the field, however are not included in most textbooks. A distinguishing feature of the book is that explicit proofs or derivations are given for all results. For some key results, two or three derivations are provided.
The material is presented as simply as possible. Reading the book does not require any previous knowledge of quantum chemistry, only some familiarity with its goals and approaches is supposed. To fully understand the book, only acquaintance with the simplest notions of quantum mechanics (the concepts of wave functions, operators and their matrix elements, the time-dependent and time-independent Schrödinger equation) as well as some basic knowledge from calculus, matrix and linear algebra are required. Any material which might be not familiar to a chemist is included either in the body of the book or in the appendices. Despite of this relative simplicity, this is a book about the formalism of quantum chemistry---about the theoretical results, their proofs or derivations---and less attention is paid to the motivations of deriving the equations discussed. In accord with that the book may be considered a textbook "from the beginning but not for beginners".
The book is intended for students and young specialists in theoretical chemistry and related areas such as spectroscopy, materials research, molecular physics etc. It will be of particular interest to those who possess some introductory background in quantum chemistry and wish to gain a deeper understanding of its lasting concepts. While the results presented in the book are essentially standard, a number of the proofs and derivations are original.