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 V(x)=g₁x^-1+g₂x^-2. For g₂>0 and g₁<0, 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 V(x) 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.