Quantum Mechanics

An Introduction for Physicists

https://doi.org/10.1142/14057 | May 2025

Pages: 400

By (author):
Torsten Fliessbach (University of Siegen, Germany)

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ISBN: 978-981-98-0137-4 (hardcover) USD 148.00 Add to cart

This book on Quantum Mechanics starts with the known field equation of Electrodynamics. Then comes the following steps: in the case of very weak fields the electromagnetic field equation becomes the quantum mechanical wave equation for single photons. This equation is generalized for massive particles (Klein–Gordon equation). The non-relativistic limit of this is the free Schrödinger equations. In this way the correspondence rules (leading from the Hamilton function to the Hamilton operator) are motivated.

On the whole, this book concentrates on applications, and on how things can be calculated . The formal structures are treated to the necessary extent.

The applications include all standard topics (including alpha-decay, the hydrogen atom including relativistic correction, angular moment coupling, the Stark effect) and proceed to many-body problems. This includes an introduction of the shell model of the atom and that of the atomic nucleus.

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Contents:

Schrödinger's Wave Mechanics:
- Wave-Particle Duality
- Free Schrödinger Equation
- Schrödinger Equation
- Normalization
- Expectation Values
- Hermitian Operators
- Uncertainty Relation
- Measurement Process and Uncertainty Relation
Eigenvalues and Eigenfunctions:
- Solution of The Free Schrödinger Equation
- Time Independent Schrödinger Equation
- Infinite Square Well Potential
- One-Dimensional Oscillator
- Three-Dimensional Oscillator
- Completeness and Orthonormalization
- Time Evolution
- Operator and Observable
- Symmetry and Conservation Laws
One-Dimensional Problems:
- Potential Barrier
- Delta Potential
- Potential Box
- WKB Approximation
- Alpha Decay
Three-Dimensional Problems:
- Angular Momentum Operator
- Central Force Problem
- Box Potential
- Scattering: General Aspects
- Scattering: Applications
- Spherical Oscillator
- Hydrogen Atom
Abstract Formulation:
- Hilbert Space
- Operators in Hilbert Space
- Unitary Transformations
- Representations of the Schrödinger Equation
Operator Method:
- Oscillator with Operator Method
- Heisenberg Picture
- Angular Momentum with Operator Method
- Spin
- Coupling of Angular Momenta
Approximation Methods:
- 39 Time Independent Perturbation Theory
- Stark Effect
- Relativistic Corrections in the Hydrogen Atom
- Time Dependent Perturbation Theory
- Radiation of Atoms
- Variational Approach
- Born Approximation
Many-Body Systems:
- Many-Body Wave Function
- Ideal Fermi Gas
- Atoms
- Molecules

Readership: Undergraduates in physics.

Torsten Fliessbach is the Professor for Theoretical Physics, since 1979, at the University of Siegen, Germany. Born in Lauenburg (Pommern, Germany), he obtained his high school diploma (Abitur) at the Altes Realgymnasium in Munich, and his Diploma in Physics (1968) and PhD (1971) at the Technical University of Munich (TUM). He was awarded the scholarship of Studienstiftung des Deutschen Volkes (1966–1969) and, from 1971 to 1978, he worked as a research assistant at the Physics Department of TUM. From 1974 to 1975, Fliessbach was offered a research stint at the Lawrence Berkeley Laboratory (CA, USA) under the fellowship, Deutsche Forschungsgemeinschaft. In 1977, he was conferred Habilitation at TUM and, from 1978 to 1979, he was offered the Heisenberg fellowship. Prof. Fliessbach is especially known for authoring a series of textbooks in theoretical physics (first editions, in German), spanning the subjects on General Relativity, Mechanics, Electrodynamics, Quantum Mechanics and Statistical Physics.

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Quantum Mechanics