INVESTIGADORES
GONZALEZ PISANI Pablo Andres
congresos y reuniones científicas
Título:
Extensiones Autoadjuntas del Hamiltoniano de un Sistema de Fermiones
Autor/es:
H. FALOMIR AND P.A.G. PISANI
Lugar:
Buenos Aires
Reunión:
Congreso; 85a Reunión Anual de la A.F.A.; 2000
Institución organizadora:
Asociación Física Argentina
Resumen:
We study the stationary problem of a charged Dirac particle in (2+1)
dimensions in the presence of a uniform magnetic field B and a singular
magnetic tube of flux Φ = 2πκ/e. The rotational invariance
of this configuration implies that the subspaces of definite angular
momentum l + 1/2 are invariant under the action of the Hamiltonian H. We
show that for κ-l≥1 or κ-l≤0 the restriction of H to
these subspaces, Hl, is essentially self-adjoint, while for
0<κ-l<1 Hl admits a one-parameter family of
self-adjoint extensions (SAEs). In the latter case, the functions in the
domain of Hl are singular (but square integrable) at the
origin, their behaviour being dictated by the value of the parameter
γ that identifies the SAE. We also determine the spectrum of the
Hamiltonian as a function of κ and γ, as well as its
closure.