TY  - BOOK
AU  - Hall,Brian C.
TI  - Quantum theory for mathematicians 
T2  - Graduate texts in mathematics,
SN  - 9781461471158 (acidfree paper)
AV  - QC174.12 .H346 2013
U1  - 530.12 H174Q 23
PY  - 2013///
CY  - New York
PB  - Springer
KW  - Quantum theory
KW  - Mathematics
KW  - fast
KW  - Quantenmechanik
KW  - gnd
KW  - Mathematische Methode
N1  - Includes bibliographical references (pages 545-548) and index; The experimental origins of quantum mechanics; Is light a wave or a particle?; Is an electron a wave or a particle?; Schrödinger and Heisenberg; A matter of interpretation; Exercises --; A first approach to classical mechanics; Motion in R¹; Motion in R[superscript n]; Systems of particles; Angular momentum; Poisson brackets and Hamiltonian mechanics; The Kepler problem and the Runge-Lenz vector; Exercises --; First approach to quantum mechanics; Waves, particles, and probabilities; A few words about operators and their adjoints; Position and the position operator; Momentum and the momentum operator; The position and momentum operators; Axioms of quantum mechanics : operators and measurements; Time-evolution in quantum theory; The Heisenberg picture; Example : a particle in a box; Quantum mechanics for a particle in R [superscript n]; Systems of multiple particles; Physics notation; Exercises --; The free Schrödinger equation; Solution by means of the Fourier transform; Solution as a convolution; Propagation of the wave packet : first approach; Propagation of the wave packet : second approach; Spread of the wave packet; Exercises --; Particle in a square well; The time-independent Schrödinger equation; Domain questions and the matching conditions; Finding square-integrable solutions; Tunneling and the classically forbidden region; Discrete and continuous spectrum; Exercises --; Perspectives on the spectral theorem; The difficulties with the infinite-dimensional case; The goals of spectral theory; A guide to reading; The position operator; Multiplication operators; The momentum operator --; The spectral theorem for bounded self-adjoint operators : statements; Elementary properties of bounded operators; Spectral theorem for bounded self-adjoint operators, I; Spectral theorem for bounded self-adjoint operators, II; Exercises --; The spectral theorem for bounded self-adjoint operators : proofs; Proof of the spectral theorem, first version; Proof of the spectral theorem, second version; Exercises --; Unbounded self-adjoint operators; Introduction; Adjoint and closure of an unbounded operator; Elementary properties of adjoints and closed operators; The spectrum of an unbounded operator; Conditions for self-adjointness and essential self-adjointness; A counterexample; An example; The basic operators of quantum mechanics; Sums of self-adjoint operators; Another counterexample; Exercises --; The spectral theorem for unbounded self-adjoint operators; Statements of the spectral theorem; Stone's theorem and one-parameter unitary groups; The spectral theorem for bounded normal operators; Proof of the spectral theorem for unbounded self-adjoint operators; Exercises --; The harmonic oscillator; The role of the harmonic oscillator; The algebraic approach; The analytic approach; Domain conditions and completeness; Exercises --; The uncertainty principle; Uncertainty principle, first version; A counterexample; Uncertainty principle, second version; Minimum uncertainty states; Exercises --; Quantization schemes for Euclidean space; Ordering ambiguities; Some common quantization schemes; The Weyl quantization for R²[superscript n]; The "No go" theorem of Groenewold; Exercises --; The Stone-Von Neumann theorem; A heuristic argument; The exponentiated commutation relations; The theorem; The Segal-Bargmann space; Exercises --; The WKB approximation; Introduction; The old quantum theory and the Bohr-Sommerfeld condition; Classical and semiclassical approximations; The WKB approximation away from the turning points; The Airy function and the connection formulas; A rigorous error estimate; Other approaches; Exercises --; Lie groups, Lie algebras, and representations; Summary; Matrix Lie groups; Lie algebras; The matrix exponential; The Lie algebra of a matrix Lie group; Relationships between Lie groups and Lie algebras; Finite-dimensional representations of Lie groups and Lie algebras; New representations from old; Infinite-dimensional unitary representations; Exercises --; Angular momentum and spin; The role of angular momentum in quantum mechanics; The angular momentum operators in R³; Angular momentum from the Lie algebra point of view; The irreducible representations of so(3); The irreducible representations of SO(3); Realizing the representations inside L²(S²) --; Realizing the representations inside L²(M³); Spin; Tensor products of representations : "addition of angular momentum"; Vectors and vector operators; Exercises --; Radial potentials and the hydrogen atom; Radial potentials; The hydrogen atom : preliminaries; The bound states of the hydrogen atom; The Runge-Lenz vector in the quantum Kepler problem; The role of spin; Runge-Lenz calculations; Exercises --; Systems and subsystems, multiple particles; Introduction; Trace-class and Hilbert-Schmidt operators; Density matrices : the general notion of the state of a quantum system; Modified axioms for quantum mechanics; Composite systems and the tensor product; Multiple particles : bosons and fermions; "Statistics" and the Pauli exclusion principle; Exercises --; The path integral formulation of quantum mechanics; Trotter product formula; Formal derivation of the Feynman path integral; The imaginary-time calculation; The Wiener measure; The Feynman-Kac formula; Path integrals in quantum field theory; Exercises --; Hamiltonian mechanics on manifolds; Calculus on manifolds; Mechanics on symplectic manifolds; Exercises --; Geometric quantization on Euclidean space; Introduction; Prequantization; Problems with prequantization; Quantization; Quantization of observables; Exercises --; Geometric quantization on manifolds; Introduction; Line bundles and connections; Prequantization; Polarizations; Quantization without half-forms; Quantization with half-forms : the real case; Quantization with half-forms : the complex case; Pairing maps; Exercises --; A review of basic material; Tensor products of vector spaces; Measure theory; Elementary functional analysis; Hilbert spaces and operators on them
ER  -