  An analytical solution of the quantum problem of an electron on a spherical
segment with angular confinement potential of the form of rectangular
impenetrable walls is presented. It is shown that the problem is reduced to
finding solution of hypergeometric equation. As an application of the obtained
results the quantum transitions in this system are discussed, and it is shown
that the selection rule for quantum number l is removed due to the violation of
spherical symmetry of the problem.
