Bound states of massive fermions in Aharonov–Bohm-like fields

Abstract

Bound states of massive fermions in AharonovBohm (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 selfadjoint 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.

Relativistic quantum dynamics of a neutral particle in external electric fields: An approach on effects of spin

“…The AC effect and consequently the AB effect also has been addressed to bound states. In the context of the method of operators in quantum mechanics such bound states are found by modeling the problem by boundary conditions at the origin [12][13][14][15][16][17][18][19][20][21][22][23] (See also Refs. [24][25][26][27] where bound states also are obtained for Aharonov-Bohm-like systems.…”

Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions

“…In this work, by using the self-adjoint extension approach, we shall confirm these results and show that this delta function also leads to bound states. This approach had to be adopted to deal with singular Hamiltonians in previous works as, for example, in the study of spin 1/2 AB system and cosmic strings [5,65], in the Aharonov-Bohm-Coulomb problem [33,34,66,67], and the study of the equivalence between the self-adjoint extension method and renormalization [29].…”

Quantum states of a neutral massive fermion with an anomalous magnetic moment in an Aharonov–Casher field

“…For −∞ < ξ < 0, there exist bound fermion states (see, also [9]). In order for a quantum system to have a bound state, its energy must be negative, and, therefore, discrete levels with E < 0 have to exist in addition to continuous part of the energy spectrum.…”

“…We note that self-adjoint Hamiltonians with the AB potential and ACF have been considered to show the presence of fermion bound states in [4][5][6][7][8][9][10]. Self-adjoint Schrödinger and Dirac Hamiltonians with singular potentials (such as the one-dimensional Calogero potential, the Coulomb potential, a superposition of the Aharonov-Bohm field and the so-called magnetic-solenoid field and the potentials localized at the origin, in particular, delta-like potentials) were considered in many works (see [5] and references there).…”