|
Journal of Physical Studies 10(2), 81–85 (2006)
DOI: https://doi.org/10.30970/jps.10.81 PAULI EQUATION WITH POSITION-DEPENDENT MASSV. M Tkachuk, S. I. Vakarchuk
Department for Theoretical Physics, Ivan Franko National University of
Lviv, |
 |
The motion of electron with position-dependent mass is studied. For three dimensional space with a spherically symmetric dependence of mass on coordinates there exists supersymmetry with two, three and four supercharges similarly to constant mass. In the two dimensional case the supersymmetry with two supercharges exists for an arbitrary dependence of mass on position and an arbitrary magnetic field, which is perpendicular to the plane of electron motion. For the latter case and an axially symmetric dependence of mass on coordinates exact wave functions for zero energy ground state are found. The number of zero modes for an electron with position dependent mass in magnetic field is found as well. This result is the generalization of Aharonov-Casher theorem obtained for constant mass for the case of position dependent mass.
PACS number(s): 03.65.-w, 11.30.Pb