Abstract
An analytical solution of the quantum problem of an electron on a spherical segment with angular confinement potential in the form of rectangular impenetrable walls is presented. It is shown that the problem is reduced to finding solution of hypergeometric equation. On the basis of the obtained results the optical interband transitions in this system are discussed, and the threshold frequency and absorption coefficient both for single structure and non-interacting ensemble are calculated. The influence of electric field on system is discussed and it is shown that in such type of structure linear Stark shift takes place. Quantum transitions in the presence of electric field are considered and it is shown that the selection rule for an orbital quantum number analogue is removed.
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