Quantum ring on sphere: Electron states on spherical segment

Quantum problem of electron on a spherical segment is discussed. The confinement potential of segment is chosen in the form of singular analog of CP1-oscillator. The exact solution of quantum problem of electron states in a quantum ring on a spherical surface is done. Analytical expressions for the wave functions and energy spectrum are found. The ground state energy at different values of the confining potential parameters is calculated numerically in the case of impenetrable walls. Its dependence on the limitation angles is shown. Transition to the case of an alternative model of a spherical oscillator is discussed.