Symmetry of time-dependent Schrödinger equations. I. A classification of time-dependent potentials by their maximal kinematical algebras

DOI10.1063/1.525142zbMath0475.35038OpenAlexW2053312632MaRDI QIDQ3931764

D. Rodney Truax

Publication date: 1981

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525142

zbMATH Keywords

time-dependent Schrödinger equationtime-dependent harmonic oscillatorLie symmetry algebradynamical algebra

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) General quantum mechanics and problems of quantization (81S99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (13)

On form-preserving transformations for the time-dependent Schrödinger equation ⋮ SCHRÖDINGER EQUATIONS WITH TIME-DEPENDENT P² AND X² TERMS ⋮ Global \(\widetilde{\text{SL}(2,R)}\) representations of the Schrödinger equation with singular potential ⋮ On a time-dependent extension of the Morse potential ⋮ Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations ⋮ Time-dependent Schrödinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states ⋮ Displacement-operator squeezed states. I. Time-dependent systems having isomorphic symmetry algebras ⋮ Displacement-operator squeezed states. II. Examples of time-dependent systems having isomorphic symmetry algebras ⋮ Squeezed states for general systems ⋮ Symmetry of the Schrödinger Equation with Variable Potential ⋮ Resonance Broadening Theory of Farley-Buneman Turbulence in the Auroral E-Region ⋮ Form-preserving transformations for Hamiltonians with linear terms in the momentum ⋮ Symmetry of time-dependent Schrödinger equations. II. Exact solutions for the equation {∂x x+2i∂t−2g2(t)x2−2g1(t)x −2g0(t)}Ψ(x, t) = 0

Cites Work

• Dynamical symmetries of rotationally invariant, three-dimensional, Schrödinger equations
• The complete symmetry group of the one-dimensional time-dependent harmonic oscillator
• Symmetry breaking interactions for the time dependent Schrödinger equation
• Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0

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