Kok P. Advanced Quantum Mechanics 2024

Textbook in PDF format

The modern version of quantum mechanics was formulated in 1932 by John von Neumann in his famous book Mathematical Foundations of Quantum Mechanics, and it unifies Schrödingers wave theory with the matrix mechanics of Heisenberg, Born, and Jordan. The theory is framed in terms of linear vector spaces, so we also have to remind ourselves of the relevant mathematics. The entire structure of quantum mechanics (including its relativistic extension) can be formulated in terms of states and operations in Hilbert space. We need rules that map the physical quantities such as states, observables, and measurements to the mathematical structure of vector spaces, vectors and operators. There are several ways in which this can be done.
Linear Vector Spaces and Hilbert Space
The Postulates of Quantum Mechanics
Schrödinger and Heisenberg Pictures
Mixed States and the Density Operator
Composite Systems and Entanglement
Evolution of Open Quantum Systems
Orbital Angular Momentum and Spin
Identical Particles
Many-Body Problems in Quantum Mechanics
Pauli Spin Matrices
Noncommuting Operators and Uncertainty
Multiple Particle States
The Schrödinger Equation
Atomic Orbitals
The Periodic Table of the Elements
Matter