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

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

1995-07-20

arxiv.org/abs/solv-int/9507003v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

21 pages, latex, to appear in the "Journal of Mathematical Physics" (1995)

Scientific paper

10.1063/1.531274

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schr\" odinger equation with the anisotropic harmonic oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schr\" odinger equation ($V=0$).

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