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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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