Books like Matrix mechanics by Herbert S. Green

A comprehensive, second‑edition text on quantum mechanics that refreshes the mathematical foundation, explores time‑reversal invariance, and delivers an extensive treatment of path integrals for advanced undergraduates and graduate students.

This is one of the most clear presentations of Quantum Mechanics (QM). Starting with a simple motivation for the need of a theory beyond classical physics, Dirac describes a number of features required in the new theory (QM), and proceeds to delineate properties which physical states (quantum states) have to obey in order to make sense in the observable world.

The text proceeds to develop the standard QM terminology (state vector, operator, observable, equation of motion) and delves then into idealized and real physical systems (harmonic oscillator, free particle, hydrogen atom). The latter part of the book covers advanced topics like perturbation theory, scattering problems, multi-particle systems, relativistic systems. Only the chapter on Quantum Electro Dynamics might be considered to short by modern standards, but certainly serves as a good introduction.

Paul Dirac, the author of this masterwork, is one of the founders of Quantum Mechanics. Mainly known today for the Dirac Equation, he can be considered one of the early Quantum Physicists who presented a complete picture of the mathematical foundations of the then new theory. His 'Principles' has withstood the test of time, and is as valuable a resource today as it was in the 1930s.

"Thoroughly revised, updated, and expanded by more than one third, this new edition of Golub and Van Loan's landmark book in scientific computing provides the vital mathematical background and algorithmic skills required for the production of numerical software. New chapters on high performance computing use matrix multiplication to show how to organize a calculation for vector processors as well as for computers with shared or distributed memories. A.so new are discussions of parallel vector methods for linear equations, least squares, and eigenvalue problems."--Back cover.