Some Conservative Force Field Potentials In Scattering Theory
Abstract
In this paper we use the Lie symmetry method to calculate the universal group of symmetry transformations for the 3-dimensional time dependent Schr¨odinger wave equation. It is shown that this system admits a subgroup of SL(6,R) as symmetry group. Invariance properties of this group are used to construct solutions to the wave equation with a coloumbic force field potential. New solutions are thus obtained which are useful in scattering theory. Furthermore, it is shown that an application of the symmetry group to the set of states S = Hˆ (H complex Hilbert space) of the system preserves transition probabilities as well as the dynamics of the system.
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