On the new approach to variable separation in the time-dependent Schrödinger equation with two space dimensions

DOI10.1063/1.531274zbMath0843.35096arXivsolv-int/9507003OpenAlexW3103739356MaRDI QIDQ4873447

Renat Zhdanov, W. I. Fushchich, I. V. Revenko

Publication date: 15 August 1996

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

Full work available at URL: https://arxiv.org/abs/solv-int/9507003

zbMATH Keywords

anisotropic harmonic oscillator potentialseparation of variables in the Schrödinger equation

Mathematics Subject Classification ID

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

Related Items (7)

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 ⋮ Separation of variables in (1+2)-dimensional Schrödinger equations ⋮ On separable Schrödinger–Maxwell equations ⋮ Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source ⋮ On separable Schrödinger equations

Cites Work

• 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
• Separation of variables in the nonlinear wave equation

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