Second Quantized Approach to Quantum Chemistry: An Elementary Introduction

✍ Scribed by Péter R. Surján (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1989
• Tongue: English
• Leaves: 196
• Edition: 1
• Category: Library

✦ Synopsis

The aim of this book is to give a simple, short, and elementary introduction to the second quantized formalism as applied to a many-electron system. It is intended for those, mainly chemists, who are familiar with traditional quantum chemistry but have not yet become acquainted with second quantization. The treatment is, in part, based on a series of seminars held by the author on the subject. It has been realized that many quantum chemists either interested in theory or in applications, being educated as chemi~ts and not as physicists, have never devoted themselves to taking a course on the second quantized approach. Most available textbooks on this topic are not very easy to follow for those who are not trained in theory, or they are not detailed enough to offer a comprehensive treatment. At the same time there are several papers in quantum chemical literature which take advantage of using second quantization, and it would be worthwhile if those papers were accessible for a wider reading public. For this reason, it is intended in this survey to review the basic formalism of second quantization, and to treat some selected chapters of quantum chemistry in this language. Most derivations will be carried out in a detailed manner, so the reader need not accept gaps to understand the result.

✦ Table of Contents

Front Matter....Pages I-XIII
Introduction....Pages 1-5
The Concept of Creation and Annihilation Operators....Pages 6-17
Particle Number Operators....Pages 18-21
Second Quantized Representation of Quantum-Mechanical Operators....Pages 22-32
Evaluation of Matrix Elements....Pages 33-39
Advantages of Second Quantization—Illustrative Examples....Pages 40-45
Density Matrices....Pages 46-52
Connection to “Bra and Ket” Formalism....Pages 53-58
Using Spatial Orbitals....Pages 59-65
Some Model Hamiltonians in Second Quantized Form....Pages 66-86
The Brillouin Theorem....Pages 87-92
Many-Body Perturbation Theory....Pages 93-102
Second Quantization for Nonorthogonal Orbitals....Pages 103-113
Second Quantization and the Hellmann-Feynman Theorem....Pages 114-120
Intermolecular Interactions....Pages 121-136
Quasiparticle Transformations....Pages 137-152
Miscallenous Topics Related to Second Quantization....Pages 153-162
Problem Solutions....Pages 163-174
References....Pages 175-179
Back Matter....Pages 181-184

✦ Subjects

Theoretical and Computational Chemistry;Quantum Information Technology, Spintronics;Quantum Physics