  We present a new exactly solvable quantum problem for which the Schroedinger
equation allows for separation of variables in oblate spheroidal coordinates.
Namely, this is the quantum mechanical two Coulomb centers problem for the case
of imaginary intercenter parameter and complex conjugate charges is considered.
Since the potential is defined by the two-sheeted mapping whose singularities
are concentrated on a circle rather than at separate points, there arise
additional possibilities in choice of boundary conditions. Detailed
classification of the various types of boundary-value problems is given. The
quasi-radial equation leads to a new type of boundary value problems which was
never considered before. Results of the numerical calculations allowing to draw
conclusions about the structure of the energy spectrum are shown. Possible
physical applications are discussed.
