On separable Schrödinger equations

@inproceedings{Zhdanov1999OnSS,
  title={On separable Schr{\"o}dinger equations},
  author={R. Sh. Zhdanov and Alexander Zhalij},
  year={1999}
}
We classify (1+3)-dimensional Schrödinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a result, we get eleven classes of the electromagnetic vector potentials of the electromagnetic field A(t, ~x) = (A0(t, ~x), ~ A(t, ~x)) providing separability of the corresponding Schrödinger equations. It is established, in particular, that the necessary condition for the Schrödinger equation to be separable is that the… CONTINUE READING
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