On form-preserving transformations for the time-dependent Schrödinger equation

DOI10.1063/1.532885zbMath0945.35025arXivmath-ph/9809013OpenAlexW3101268492MaRDI QIDQ4270343

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Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/math-ph/9809013

zbMATH Keywords

Darboux transformationpoint transformations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Schrödinger operator, Schrödinger equation (35J10)

Related Items (19)

SEPARATION OF COUPLED SYSTEMS OF SCHRODINGER EQUATIONS BY DARBOUX TRANSFORMATIONS ⋮ Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials ⋮ Freezable bound states in the continuum for time-dependent quantum potentials ⋮ Study of uncertainty, average energy, and thermodynamic quantities of the time dependent quantum system ⋮ The Black-Scholes equation in finance: quantum mechanical approaches ⋮ Burgers equation with time-dependent coefficients and nonlinear forcing term: linearization and exact solvability ⋮ A class of exactly solvable Schrödinger equation with moving boundary condition ⋮ Form-preserving transformations for the time-dependent Schrödinger equation in \((n+1)\) dimensions ⋮ Intertwined isospectral potentials in an arbitrary dimension ⋮ EFFECTIVE MASS HAMILTONIANS WITH LINEAR TERMS IN THE MOMENTUM: DARBOUX TRANSFORMATIONS AND FORM-PRESERVING TRANSFORMATIONS ⋮ DARBOUX TRANSFORMATIONS FOR TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS ⋮ Infinite Square-Well, Trigonometric Pöschl-Teller and Other Potential Wells with a Moving Barrier ⋮ Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners ⋮ REALITY CONDITION FOR DARBOUX TRANSFORMATIONS OF TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS ⋮ Point Transformations: Exact Solutions of the Quantum Time-Dependent Mass Nonstationary Oscillator ⋮ Darboux transformations for Schrödinger equations in two variables ⋮ Form-preserving transformations for Hamiltonians with linear terms in the momentum ⋮ Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians ⋮ Average energy and quantum similarity of a time dependent quantum system subject to Pöschl-Teller potential

Cites Work

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• Supersymmetric transformations of real potentials on the line
• On Mapping Linear Partial Differential Equations to Constant Coefficient Equations
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• On the Transformation of Diffusion Processes into the Wiener Process
• Symmetry of time-dependent Schrödinger equations. I. A classification of time-dependent potentials by their maximal kinematical algebras
• Inverse scattering on the line
• The evolution operator technique in solving the Schrodinger equation, and its application to disentangling exponential operators and solving the problem of a mass-varying harmonic oscillator
• New classes of Schrödinger equations equivalent to the free particle equation through non-local transformations
• Unitary transformation approach to the exact solutions of time-dependent quantum systems withSU(1, 1) dynamical group
• Quantum motion in a Paul trap
• Lie Algebraic Solution of Linear Differential Equations
• On the exponential solution of differential equations for a linear operator

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