871 research outputs found
Dirac equation in the magnetic-solenoid field
We consider the Dirac equation in the magnetic-solenoid field (the field of a
solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm
solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using
von Neumann's theory of deficiency indices. We find self-adjoint extensions of
the Dirac Hamiltonian in both above dimensions and boundary conditions at the
AB solenoid. Besides, for the first time, solutions of the Dirac equation in
the magnetic-solenoid field with a finite radius solenoid were found. We study
the structure of these solutions and their dependence on the behavior of the
magnetic field inside the solenoid. Then we exploit the latter solutions to
specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm
solenoid.Comment: 23 pages, 2 figures, LaTex fil
Self-adjoint extensions and spectral analysis in the generalized Kratzer problem
We present a mathematically rigorous quantum-mechanical treatment of a
one-dimensional nonrelativistic motion of a particle in the potential field
. For and , the potential is
known as the Kratzer potential and is usually used to describe molecular energy
and structure, interactions between different molecules, and interactions
between non-bonded atoms. We construct all self-adjoint Schrodinger operators
with the potential and represent rigorous solutions of the corresponding
spectral problems. Solving the first part of the problem, we use a method of
specifying s.a. extensions by (asymptotic) s.a. boundary conditions. Solving
spectral problems, we follow the Krein's method of guiding functionals. This
work is a continuation of our previous works devoted to Coulomb, Calogero, and
Aharonov-Bohm potentials.Comment: 31 pages, 1 figur
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