On Separable Schrödinger Equations

@article{Zhdanov1999OnSS,
  title={On Separable Schr{\"o}dinger Equations},
  author={Renat Z. Zhdanov and Alexander Zhalij},
  journal={Mathematics eJournal},
  year={1999}
}
We classify (1+3)-dimensional Schrodinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a result, we get 11 classes of the vector potentials of the electromagnetic field A(t,x)=(A0(t,x),A(t,x)) providing separability of the corresponding Schrodinger equations. It is established, in particular, that the necessary condition for the Schrodinger equation to be separable is that the magnetic field must be… 

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