Quantum States of a Neutral Massive Fermion with an Anomalous Magnetic Moment in an External Electric Fieldстатья
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Дата последнего поиска статьи во внешних источниках: 4 сентября 2018 г.
Аннотация:Abstract—The quantum dynamics of a nonrelativistic neutral massive fermion with an anomalous magnetic
moment (AMM) is examined in the external electric field of an infinitely long thin homogeneously charged
thread in the plane with a normal directed along the thread. The Hamiltonian of the Dirac–Pauli equation
for a neutral fermion with AMM is essentially singular in the considered external field and requires a supple
mentary
extension of the definition in order for it to be treated as a self-adjoint quantum-mechanical opera
tor.
All one-parameter self-adjoint extensions of the Hamiltonian of the Dirac–Pauli equation in the consid
ered
external field are found in the nonrelativistic approximation. The corresponding Hilbert space of square
integrable
functions, including a singularity point of the Hamiltonian, is specified for each self-adjoint exten
sion
of the Hamiltonian. The wave functions of free and bound states, as well as discrete energy levels, are
determined by the self-adjoint extension method and their correspondence with similar quantities obtained
by the physical regularization procedure is discussed. It is shown that energy levels of bound states are simple
poles of the scattering amplitude, which should be extended in definition by introducing the self-adjoint
extension parameter into it. Expressions for the scattering amplitude and cross-section, depending on the ori
entation
of the initial-state spin of fermion, are obtained.