Mathematical Concepts of Quantum MechanicsSpringer Science & Business Media, 2003 - 249 pages The book gives a streamlined introduction to quantum mechanics, while describing the basic mathematical structures underpinning this discipline. Starting with an overview of the key physical experiments illustrating the origin of the physical foundations, the book proceeds to a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The topics presented include spectral theory, many-body theory, positive temperatures, path integrals and quasiclassical asymptotics, the theory of resonances, an introduction to quantum field theory and the theory of radiation. The book can serve as a text for an intermediate course in quantum mechanics, or a more advanced topics course. |
Table des matières
I | 6 |
II | 16 |
III | 30 |
IV | 36 |
V | 61 |
VI | 69 |
VII | 81 |
VIII | 103 |
X | 145 |
XI | 151 |
XII | 167 |
XIII | 185 |
XIV | 199 |
XV | 231 |
XVI | 241 |
XVII | 267 |
Autres éditions - Tout afficher
Mathematical Concepts of Quantum Mechanics Stephen J. Gustafson,Israel Michael Sigal Aperçu limité - 2011 |
Mathematical Concepts of Quantum Mechanics Stephen J. Gustafson,Israel Michael Sigal Aperçu limité - 2012 |
Expressions et termes fréquents
assume asymptotic atom Banach space boundary conditions bounded operator called Chapter classical path compute consider corresponding critical point defined definition denote derivative differentiable Dirichlet boundary conditions dynamics eigenfunctions eigenvalues essential spectrum evolution example fact field theory finite Fock space follows formula Fourier transform ground state energy Hamiltonian Hence Hilbert space Ho(ɛ Hpart implies integral kernel interaction invertible isospectral Klein-Gordon L²(Rd Lemma linear Mathematical Supplement matrix minimizer momentum multiplication nonlinear normalized notation number of particles obtain operator H orthogonal projection orthonormal path integral perturbation phase Phys physics Poisson bracket potential V(x Problem proof properties prove quantization quantum mechanics RanP Recall relation resonance right hand side satisfies Schrödinger equation Schrödinger operator Section self-adjoint operator solutions spectral stationary subspace Theorem trace class variables vector wave function Weyl sequence zero