Separation of variables in (1+2)-dimensional Schrödinger equations

DOI10.1063/1.531874zbMath0872.35093OpenAlexW1979897394MaRDI QIDQ4338368

Renat Zhdanov

Publication date: 3 July 1997

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

Full work available at URL: https://semanticscholar.org/paper/c8b4877e0d944156d97bdf5709991d4e7f5dfe87

zbMATH Keywords

Schrödinger equationsFokker-Planck equations

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (9)

On separable Pauli equations ⋮ Functionally separable solutions to nonlinear wave equations by group foliation method ⋮ Functional Separable Solutions to Nonlinear Diffusion Equations by Group Foliation Method ⋮ Nonlinear evolution equations admitting multilinear variable separable solutions ⋮ Bäcklund transformations and solutions of some generalized nonlinear evolution equations ⋮ On separable Schrödinger–Maxwell equations ⋮ Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source ⋮ On separable Schrödinger equations ⋮ Multidimensional quasi-exactly solvable potentials with two known eigenstates

Cites Work

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• New similarity reductions of the Boussinesq equation
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• Killing Tensors and Nonorthogonal Variable Separation for Hamilton–Jacobi Equations
• Lie theory and separation of variables. 6. The equation i U t + Δ2U = 0
• Lie Theory and Separation of Variables for the Equation \[ iU_t + \Delta _2 U - \left( {\frac{\alpha }{{x_1^2 }} + \frac{\beta }{{x_2^2 }}} \right)U = 0\]
• Orthogonal and non-orthogonal separation of variables in the wave equation u_tt-u_xx+V(x)u=0u_tt-u_xx+V(x)u=0
• Direct reduction and differential constraints
• Antireduction and exact solutions of nonlinear heat equations
• Conditional Lie-Backlund symmetry and reduction of evolution equations
• Separation of variables in two-dimensional wave equations with potential
• Separation of variables in the nonlinear wave equation
• On the new approach to variable separation in the time-dependent Schrödinger equation with two space dimensions

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