A course on Introductory Quantum Theory

✍ Scribed by Reinhard Hentsche

• Publisher: Bergische Universität Wuppertal
• Year: 2016
• Tongue: English
• Leaves: 137
• Category: Library

✦ Synopsis

These lecture notes cover introductory quantum theory to an extend that can be presented in a one semester course. The subject is approached by looking first at some of the pressing questions by the end of the 19th century, when classical physics, in the eyes of many, had come close to explaining all known physical phenomena. We will focus on a special question (e.g. the black body problem), then introduce an idea or concept to answer this question in simple terms (e.g. energy quantization), relate the quantum theoretical answer to classical theory or experiment, and finally progress deeper into the mathematical formalism if it provides a general basis for answering the next question. In this spirit we develop quantum theory by adding in a step by step procedure postulates and abstract concepts, testing the theory as we go along, i.e. we will accept abstract and maybe sometimes counter intuitive concepts as long as they lead to verifiable predictions.

✦ Table of Contents

1 Early developments in quantum mechanics
1.1 Quantization conditions
1.2 The black body problem
1.3 Building a general formalism
1.4 The hydrogen atom
1.5 Angular momentum algebra
2 Formal quantum mechanics
2.1 Operator averages
2.2 The uncertainty principle
2.3 From wave mechanics to matrix mechanics
2.4 The time evolution operator
2.5 The density operator
2.6 Path integration and the density operator
3 Scattering theory
3.1 The Lippmann-Schwinger equation
3.2 The 1st Born approximation
3.3 Partial wave expansion
3.4 Some remarks on formal scattering theory
4 Solution methods in quantum mechanics
4.1 Time-independent perturbations
4.2 Variation method
4.3 The quasi classical approximation
4.4 Time-dependent perturbation theory
4.5 Interaction of charges with electromagnetic fields
5 Many particle systems
5.1 Two kinds of statistics
5.2 Constructing N-particle wave functions
5.3 Electron spin
5.4 Simplified theory for helium
5.5 Simplified theory for the hydrogen molecule
5.6 Quantum mechanics in chemistry
6 The quantized radiation field and second quantization
6.1 Quantum theory of radiation
6.2 Second quantization
6.3 Interacting quantum fields:
6.4 Outlook
A Constants and units
B Mathematical appendix
B.1 Conversion to generalized coordinates
B.2 Spherical harmonics
B.3 δ-function
B.4 Fourier series and Fourier transforms
C The Casimir effect
D Problems