Chang K.L. Mathematical Structures of Quantum Mechanics

Singapore: World Scientific Publishing Company, 2011. — 207 p. — ISBN: 9814366587.This marvelous book is aimed at strengthening the mathematical background and sharpening the mathematical tools of students without rigorous training before taking the quantum mechanics course. The abstract construction of quantum postulates in the framework of Hilbert space and Hermitian operators are realized by q-representation in the formulation to demonstrate the conventional approach to quantum theory. Symmetry property is emphasized and extensively explored in this book both in continuous transformations as well as in the discrete ones. The space-time structure is discussed in depth and Dirac equation is formulated by symmetry consideration of Lorentz group.Postulates and Principles of Quantum Mechanics.
Space-Time Translation, Quantum Dynamics and Various Representations in Quantum Mechanics.
Symmetry, Transformation and Continuous Groups.
Angular Momentum.
Lorentz Transformation, O(3,1)/SL(2,C) Group and the Dirac Equation.True PDF