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
From MaRDI portal
Publication:4832791
DOI10.1063/1.1506180zbMath1060.35116OpenAlexW2057414011MaRDI QIDQ4832791
Giovanni Rastelli, C. Chanu, Sergio Benenti
Publication date: 14 December 2004
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.1506180
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40)
Related Items
Classification of the orthogonal separable webs for the Hamilton-Jacobi and Klein-Gordon equations on 3-dimensional Minkowski space ⋮ Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure ⋮ Natural star-products on symplectic manifolds and related quantum mechanical operators ⋮ The quantum harmonic oscillator on the sphere and the hyperbolic plane ⋮ 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 ⋮ Symmetric and asymmetric separation of variables for an integrable case of the complex Kirchhoff's problem ⋮ Separation of variables and superintegrability on Riemannian coverings ⋮ Systematic construction of non‐autonomous Hamiltonian equations of Painlevé‐type. III. Quantization ⋮ Miura maps for Stäckel systems ⋮ Asymmetric separation of variables for the extended Clebsch and Manakov models ⋮ Separable quantizations of Stäckel systems ⋮ Stäckel representations of stationary KdV systems ⋮ Separability in Riemannian manifolds ⋮ Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion ⋮ Exact solvability of superintegrable Benenti systems ⋮ Complex variables for separation of the Hamilton-Jacobi equation on real pseudo-Riemannian manifolds ⋮ Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional hyperbolic and de Sitter spaces ⋮ Unnamed Item ⋮ Haantjes algebras and diagonalization ⋮ Invariant classification of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space ⋮ Separability in consistent truncations ⋮ Higher order first integrals of autonomous dynamical systems ⋮ Variable-separation theory for the null Hamilton–Jacobi equation ⋮ Flat minimal quantizations of Stäckel systems and quantum separability ⋮ Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems ⋮ A new integrable system on the sphere and conformally equivariant quantization ⋮ 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 ⋮ FIXED ENERGY R-SEPARATION FOR SCHRÖDINGER EQUATION ⋮ The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds ⋮ Separability and symmetry operators for Painlevé metrics and their conformal deformations ⋮ Geodesic flows of c-projectively equivalent metrics are quantum integrable ⋮ Integrable quantum Stäckel systems ⋮ Quantum integrability of quadratic Killing tensors ⋮ New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates ⋮ Higher Haantjes brackets and integrability ⋮ Haantjes structures for the Jacobi-Calogero model and the Benenti systems
Cites Work
- Killing tensors and the separation of the Hamilton-Jacobi equation
- Separable systems of Stäckel
- The super-separability of the three-body inverse-square Calogero system
- Variable separation for natural Hamiltonians with scalar and vector potentials on Riemannian manifolds
- Killing Tensors and Variable Separation for Hamilton-Jacobi and Helmholtz Equations
- Killing Tensors and Nonorthogonal Variable Separation for Hamilton–Jacobi Equations
- Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
- On separable Schrödinger equations
- 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