Gauge variant symmetries for the Schrodinger equation

摘要

The last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative We derive the Schiodinger equation for a one-degree-of-freedom system with a constant multiplier In the sequel we consider the particular example of the simple harmonic oscillator, In the case of the general equation for the simple harmonic oscillator which contains an arbitrary function we show that all Schrodinger equations possess the same number of Lie point symmetries with the same algebra From the symmetries we construct the solutions of the Schrodinger equation and find that they differ only by a phase determined by the gauge.