Quantum mechanics : an introduction to the physical background and mathematical structure - Naber, Gregory L. (Berlin ; Boston : De Gruyter, 2021)
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.
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
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Mode of access: Internet via World Wide Web.
In English.
Keywords: Feynman Integral; Harmonischer Oszillator; Heisenberg Algebra; Quantenphysik; Supersymmetrie; SCIENCE / Physics / Quantum Theory; kvantová teória; harmonický oscilátor; kvantová mechanika; supersymetria; elektronické dokumenty