Abstract
Abstract
Using the algebraic approach Lie symmetries of time dependent Schrödinger equations for charged particles interacting with superpositions of scalar and vector potentials are classified. Namely, all the inequivalent equations admitting symmetry transformations with respect to continuous groups of transformations are presented. This classification is completed and includes the specification of symmetries and admissible equivalence relations for such equations. In particular, a simple mapping between the free Schrödinger equation and the repulsive oscillator is found which has a clear group-theoretical sense.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
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