FIXED ENERGY R-SEPARATION FOR SCHRÖDINGER EQUATION

DOI10.1142/S021988780600120XzbMath1114.81027arXivnlin/0512033MaRDI QIDQ5484701

Giovanni Rastelli, Claudia Maria Chanu

Publication date: 21 August 2006

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0512033

zbMATH Keywords

Schrödinger equationLaplace equationvariable separation\(R\)-separation

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 (8)

Invariant classification of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space ⋮ Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space ⋮ Laplace-type equations as conformal superintegrable systems ⋮ Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields ⋮ Superintegrable three-body systems on the line ⋮ \(R\)-separation of variables for the conformally invariant Laplace-Beltrami equation ⋮ The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds ⋮ Separability and symmetry operators for Painlevé metrics and their conformal deformations

Cites Work

• Variable-separation theory for the null Hamilton–Jacobi equation
• The general theory of R-separation for Helmholtz equations
• Conformal Killing Tensors and Variable Separation for Hamilton–Jacobi Equations
• Intrinsic characterisation of orthogonal R separation for Laplace equations
• Remarks on the connection between the additive separation of the Hamilton–Jacobi equation and the multiplicative separation of the Schrödinger equation. I. The completeness and Robertson conditions
• Remarks on the connection between the additive separation of the Hamilton–Jacobi equation and the multiplicative separation of the Schrödinger equation. II. First integrals and symmetry operators

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