On Time-Dependent Quadratic Quantum Hamiltonians

DOI10.1137/0140035zbMath0463.35042OpenAlexW2093586953MaRDI QIDQ3913772

Kurt Bernardo Wolf

Publication date: 1981

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0140035

zbMATH Keywords

integral transformsGreen's functionSchrödinger groupparabolic differential equationsgroup theoretical methodsalgebraically independent constants of the motionquadratic time-dependent hamiltoniansquantum mechanical Schrödinger equationssymplectic and Heisenberg groups

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications of group representations to physics and other areas of science (20C35) Second-order parabolic equations (35K10) General integral transforms (44A05)

Related Items

Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials, SCHRÖDINGER EQUATIONS WITH TIME-DEPENDENT P² AND X² TERMS, A geometric approach to time evolution operators of Lie quantum systems, An Introduction to Special Functions with Some Applications to Quantum Mechanics, Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation, On a hidden symmetry of quantum harmonic oscillators, Quadratic time dependent Hamiltonians and separation of variables, Quantization, symmetry, and natural polarization, Quantum integrals of motion for variable quadratic Hamiltonians, The Schrödinger system \(H=-\frac 1 2 e^{\Upsilon(t-t_0)}\partial_{xx}+\frac 1 2\omega^2 e^{-\Upsilon(t-t_0)}x^2\), Time evolution of quadratic quantum systems: evolution operators, propagators, and invariants, On integrability of nonautonomous nonlinear Schrödinger equations, On non-autonomous dynamical systems, Riccati equations and Lie series