Quantum Mechanics in Matrix Form

✍ Scribed by Günter Ludyk

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 217
• Series: Undergraduate Lecture Notes in Physics
• Edition: 1st ed. 2018
• 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

Content: Preface and introduction --
Quantum theory prior to 1925 --
Heisenberg's year 1925 --
Expansion of the matrix method --
Observables and uncertainty relations --
The harmonic oscillator --
Angular momentum --
Wolfgang Pauli and the hydrogen atom --
Spin --
Atoms in electromagnetic fields --
Many particle systems --
Equivalence of matrix and wave mechanics --
Relativistic quantum mechanics --
Solutions to problems --
The Kronecker product --
Fourier decomposition of periodic functions --
Laplace-Runge-Lenz vector --
Permutation --
Determinants --
Dirac's bra-ket notation --
Proofs of Pauli's formulas --
Physical quantities and units.

✦ Subjects

Quantum theory.;Matrix logic.