Ground state of a spin-½ charged particle in a two-dimensional magnetic field
- 1 June 1979
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 19 (6) , 2461-2462
- https://doi.org/10.1103/physreva.19.2461
Abstract
We prove that a spin-½ charged particle moving in a plane under the influence of a perpendicular magnetic field has () zero-energy states, where is the closest integer to the total flux in units of the flux quantum. The () independent wave functions are calculated explicitly. The result, which is extremely simple to prove, is an example of the Atiyah-Singer index theorem when applied to the Euclidean two-dimensional Dirac equation.
Keywords
This publication has 2 references indexed in Scilit:
- Massless excitations in pseudoparticle fieldsPhysical Review D, 1977
- The index of elliptic operators on compact manifoldsBulletin of the American Mathematical Society, 1963