Symmetries of Schroedinger equation with scalar and vector potentials

Abstract

Using the algebraic approach Lie symmetries of time dependent Schroedinger 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 Schroedinger equation and the repulsive oscillator is found which has a clear group-theoretical sense.

Misprints in Items 12, 13 of Table 4 are corrected

References in corpus (1)

• Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities

Cited by in corpus (5)

• Symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger equations
• Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups
• Symmetries of the Schroedinger-Pauli equation for neutral particles
• Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 2. Systems with dilatation and shift symmetries
• Form-preserving transformations of wave and Wigner functions