Quantum Mechanics in Matrix Form

✍ Scribed by Günter Ludyk (auth.)

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 217
• Edition: 1
• Category: Library

✦ Synopsis

This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.

✦ Table of Contents

Front Matter ....Pages i-xiii
Quantum Theory Prior to 1925 (Günter Ludyk)....Pages 1-9
Heisenberg’s Year 1925 (Günter Ludyk)....Pages 11-21
Expansion of the Matrix Method (Günter Ludyk)....Pages 23-32
Observables and Uncertainty Relations (Günter Ludyk)....Pages 33-46
The Harmonic Oscillator (Günter Ludyk)....Pages 47-57
Angular Momentum (Günter Ludyk)....Pages 59-75
Wolfgang Pauli and the Hydrogen Atom (Günter Ludyk)....Pages 77-84
Spin (Günter Ludyk)....Pages 85-104
Atoms in Electromagnetic Fields (Günter Ludyk)....Pages 105-109
Many Particle Systems (Günter Ludyk)....Pages 111-128
Equivalence of Matrix and Wave Mechanics (Günter Ludyk)....Pages 129-140
Relativistic Quantum Mechanics (Günter Ludyk)....Pages 141-154
Back Matter ....Pages 155-214

✦ Subjects

Quantum Physics