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, Diracs 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.

After receiving his PhD in 1967, Günter Ludyk habilitated and has been appointed Scientific Advisor and Professor (associate professor) of the Technical University of Berlin in 1970. In  1971 he has been a visiting professor at the Technical University of Graz/Austrial. Since 1972 he is a Full Professor at the Physics/Electrical Engineering Faculty of the University of Bremen. His area of research includes the theory of dynamical systems and the application of interval mathematics to generate high-precision results. He published various books on these topics both in German and English, e. g. "Time-Variant Discrete-Time-Systems in 1981 and "Stability of Time-Variant Discrete-Time Systems in 1985.

Preface and Introduction.- Quantum Theory Before 1925.- Heisenberg 1925.- Expansion of the Matrices Method.- Observables and Uncertainty Relations.- Harmonic Oscillator.- Pauli and the Hydrogen Atom.- Spin.- Atoms in Electromagnetic Fields.- Systems of Several Particles.- Equivalence of Matrix with Wave Mechanics.- Relativistic Quantum Mechanics.