Group classification of Schr\"odinger equations with position dependent mass
Mathematical Physics
2017-01-18 v3 math.MP
Quantum Physics
Abstract
Maximal kinematical invariance groups of Schr\"odinger equation with a position dependent mass and arbitrary potential are classified. It is demonstrated that there exist seven classes of such equations possessing non-equivalent continuous symmetry group. Three of these classes include arbitrary functions while the remaining ones are defined up to arbitrary parameters. In particular, for the case of a constant mass the class missing in the Boyer classification (Boyer C P 1974 Helv. Phys. Acta{\bf 47}, 450) is indicated. A constructive test of (non)equivalence of a PDM system to a constant mass system is proposed.
Keywords
Cite
@article{arxiv.1603.00890,
title = {Group classification of Schr\"odinger equations with position dependent mass},
author = {A. G. Nikitin and T. M. Zasadko},
journal= {arXiv preprint arXiv:1603.00890},
year = {2017}
}
Comments
signes for parameters \alpha and \gamma are corrected