Symmetry of time-dependent Schrödinger equations. I. A classification of time-dependent potentials by their maximal kinematical algebras

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Abstract
Potentials for the time-dependent Schrödinger equation [− 1/2 ∂xx +V(x,t)]Ψ(x,t) = i∂tΨ(x,t) are classified according to their space–time or kinematical algebras in a search for exactly solvable time-dependent models. In addition, it is shown that their dynamical algebras are isomorphic to their kinematical algebras on the solution space of the Schrödinger equation.