Quantum Mechanics (Book)

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Quantum Mechanics is mathematically simple compared to the previous two foundations of physics - classical mechanics and fields. It is linear, so no complicated manifolds like in mechanics or relativity. This is deceptive, but is a helpful crutch when first learning the subject. The true nature of quantum mechanics is geometric: the projective geometry of Hilbert space, geometric quantization from classical/symplectic geometry to quantum phase spaces, the moment map in symplectic geometry gives the map to the convex space of probability distributions, the bundles and connections appearing in the quantum Hall effect, and finally it is also a task to precisely interpret generalized functions, spectra of self-adjoint operators on function spaces, (projective) unitary group representations, and kernels/matrices of these general operators.

Quantum Mechanics
Landau Quantum Mechanics.jpg
Information
Author Lev Landau
Language English
Series Course of Theoretical Physics
Publisher Butterworth Heinemann
Publication Date 1977
Pages 677
ISBN-13 978-0-7506-3539-8

Applications

Complex Analysis

Complex Analysis by Lars Ahlfors.

Representation Theory

Representation Theory by William Fulton and Joe Harris.

The Theory of Unitary Group Representations

The Theory of Unitary Group Representations by George Mackey.

Generalized Functions: Properties and Operations

Generalized Functions: Properties and Operations by Israel Gel'fand and Georgi Shilov.

Generalized Functions: Spaces of Fundamental and Generalized Functions

Generalized Functions: Spaces of Fundamental and Generalized Functions by Israel Gel'fand and Georgi Shilov.

Generalized Functions: Applications of Harmonic Analysis

Generalized Functions: Applications of Harmonic Analysis by Israel Gelfand and Naum Vilenkin.

Spin Geometry

Spin Geometry by H. Blaine Lawson jr. and Marie-Louise Michelsohn.

Geometric Quantization

Geometric Quantization by Nicholas Woodhouse.

Noncommutative Geometry

Noncommutative Geometry by Alain Connes.