Quantum mechanics : an introduction to the physical background and mathematical structure / Gregory L. Naber.

Format:

Book

Author/Creator:

Naber, Gregory L., 1948- author.

Series:

De Gruyter Textbook

Language:

English

Subjects (All):

Quantum theory--Mathematics.

Quantum theory.

Quantum theory--Data processing.

Physical Description:

1 online resource (570 pages)

Place of Publication:

Berlin : Walter de Gruyter GmbH, [2021]

Summary:

This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions. The author addresses all these topics with utter mathematical rigor. The high number of instructive Appendices and numerous Remark sections supply the necessary background knowledge.

Contents:

Frontmatter

Preface

Contents

1 The classical harmonic oscillator

2 Lagrangian and Hamiltonian mechanics

3 The formalism of quantum mechanics: motivation

4 Physical background

5 Synopsis of self-adjoint operators, spectral theory and Stone’s theorem

6 The postulates of quantum mechanics

7 Canonical quantization

8 Path integral quantization

9 Sketches of some rigorous results

10 Fermionic and supersymmetric harmonic oscillators

A Gaussian integrals

B Morse lemma

C Stationary phase approximation

D Tangent and cotangent bundles

E Poisson and wave equations

F Carathéodory procedure

G Schwartz space, Fourier transform, distributions and Sobolev spaces

H Stieltjes integrals

I Unitary representations and Schur’s lemma

J Semigroups of operators

K Hilbert space tensor products

Bibliography

Index

Notes:

Description based on print version record.

ISBN:

3-11-075194-1

OCLC:

1269268626