Some Conservative Force Field Potentials In Scattering Theory

Authors

  • E. O. Ifidon DEPARTMENT OF MATHEMATICS, UNIVERSITY OF BENIN, BENIN CITY, NIGERIA.
  • E. O. Oghre DEPARTMENT OF MATHEMATICS, UNIVERSITY OF BENIN, BENIN CITY, NIGERIA.

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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Published

2021-04-08

How to Cite

Ifidon, E. O., & Oghre, E. O. (2021). Some Conservative Force Field Potentials In Scattering Theory. Journal of the Nigerian Mathematical Society, 32(1-3), 171–183. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/691

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