• DOI:10.1063/1.533095
• Corpus ID: 16721877

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}
}

• R. Zhdanov, Alexander Zhalij
• Published 12 November 1999
• Mathematics
• Mathematics eJournal

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 independent of the spatial variables. Next, we prove that any Schrodinger equation admitting variable separation into second-order ordinary differential equations can be reduced to one of the 11 separable Schrodinger equations mentioned above and carry out variable separation in the latter. Furthermore, we apply the results obtained for separating variables in the Hamilton–Jacobi equation.