Regular Article - Theoretical Physics
Bound states of massive fermions in Aharonov–Bohm-like fields
Faculty of Physics, Moscow State University, 119991, Moscow, Russia
* e-mail: email@example.com
Accepted: 12 December 2013
Published online: 23 January 2014
Bound states of massive fermions in Aharonov–Bohm (AB)-like fields have analytically been studied. The Hamiltonians with the (AB)-like potentials are essentially singular and therefore require specification of a one-parameter self-adjoint extension. We construct self-adjoint Dirac Hamiltonians with the AB potential in 2+1 dimensions that are specified by boundary conditions at the origin. It is of interest that for some range of the extension parameter the AB potential can bind relativistic charged massive fermions. The bound-state energy is determined by the AB magnetic flux and depends upon the fermion spin and extension parameter; it is a periodical function of the magnetic flux. We also construct self-adjoint Hamiltonians for the so-called Aharonov–Casher (AC) problem, show that nonrelativistic neutral massive fermions can be bound by the (AC) background, determine the range of the extension parameter in which fermion bound states exist, and find their energies as well as wave functions.
© The Author(s), 2014