The Friedrichs Extension of the Aharonov-bohm Hamiltonian on a Disc
نویسندگان
چکیده
We show that the Aharonov-Bohm Hamiltonian considered on a disc has a four-parameter family of self-adjoint extensions. Among the infinitely many self-adjoint extensions, we determine to which parameters the Friedrichs extension HF corresponds and its lowest eigenvalue is found. Moreover, we note that the diamagnetic inequality holds for HF .
منابع مشابه
Effects of on-center impurity on energy levels of low-lying states in concentric double quantum rings
In this paper, the electronic eigenstates and energy spectra of single and two-interacting electrons confined in a concentric double quantum rings with a perpendicular magnetic field in the presence of on-center donor and acceptor impurities are calculated using the exact diagonalization method. For a single electron case, the binding energy of on-center donor and acceptor impurities ar...
متن کاملThe bound state Aharonov-Bohm effect around a cosmic string revisited
When a quantum particle is confined between two impenetrable concentric cylindrical walls, threaded by a magnetic flux tube along their common axis, its energy spectrum presents a dependence on the flux. This is the so-called bound state Aharonov-Bohm effect [1]. A gravitational analogue of this effect, with a cosmic string replacing the flux tube, has been studied in references [2, 3]. This is...
متن کاملEffects of on-center impurity on energy levels of low-lying states in concentric double quantum rings
In this paper, the electronic eigenstates and energy spectra of single and two-interacting electrons confined in a concentric double quantum rings with a perpendicular magnetic field in the presence of on-center donor and acceptor impurities are calculated using the exact diagonalization method. For a single electron case, the binding energy of on-center donor and acceptor impurities ar...
متن کاملاثرات ناخالصیهای مغناطیسی بر عبور الکترون از یک نانو حلقه کوانتومی
In this paper we study the Aharonov-Bohm oscillations of transmission coefficient for an electron passing through a quantum nanoring with two identical magnetic impurities using quantum waveguide theory. It is shown that the Aharonov-Bohm oscillations are independent of the coupling constant between the electron and magnetic impurities for the singlet spin state of impurities, while for the o...
متن کاملPauli Approximations to the Self-Adjoint Extensions of the Aharonov-Bohm Hamiltonian
It is well known that the formal Aharonov-Bohm Hamiltonian operator, describing the interaction of a charged particle with a magnetic vortex, has a four-parameter family of self-adjoint extensions, which reduces to a two-parameter family if one requires that the Hamiltonian commutes with the angular momentum operator. The question we study here is which of these self-adjoint extensions can be c...
متن کامل