Darboux transformation for the nonsteady Schrödinger equation

DOI10.1007/BF00560273zbMath0938.58030MaRDI QIDQ1968912

L. A. Shekoyan, Vladislav G. Bagrov, Boris F. Samsonov

Publication date: 15 March 2000

Published in: Russian Physics Journal (Search for Journal in Brave)

zbMATH Keywords

supersymmetric quantum mechanicsDarboux transformationnonsteady one-dimensional Schrödinger equation

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Supersymmetry and quantum mechanics (81Q60) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Second-order parabolic equations (35K10) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (11)

New Exceptional Orthogonal Polynomials (EOPs) and Nonlinear Algebras Associated to the Quantum System ⋮ Quantum surfing ⋮ Bouncing in an oscillatory gravitational field ⋮ Extended Krein-Adler theorem for the translationally shape invariant potentials ⋮ EFFECTIVE MASS HAMILTONIANS WITH LINEAR TERMS IN THE MOMENTUM: DARBOUX TRANSFORMATIONS AND FORM-PRESERVING TRANSFORMATIONS ⋮ Multistep DBT and regular rational extensions of the isotonic oscillator ⋮ DARBOUX TRANSFORMATIONS FOR TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS ⋮ Infinite Square-Well, Trigonometric Pöschl-Teller and Other Potential Wells with a Moving Barrier ⋮ REALITY CONDITION FOR DARBOUX TRANSFORMATIONS OF TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS ⋮ 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

Cites Work

• Explicit solutions of the time-dependent Schrodinger equation
• Knot probability for lattice polygons in confined geometries
• Generalizes Darboux transformations: classification of inverse scattering methods for the radial Schrodinger equation
• Alternative factorization of eigenvalue problems in one dimension

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