Energy States of an Exciton in Truncated Paraboloid in the Intermediate Confinement Conditions

Abstract: Theoretical studies of bond or free quantum states dependency at nanovolume on its geometry and size are one of the most complex problems of modern physics. The boundary conditions on the nanovolume surface makes impossible an exact analytical solution. In this paper we using the parabolic coordinates had found the solution of Schrödinger equation boundary value problem with zero boundary conditions on the surface of a paraboloid of revolution and a cutting plane perpendicular to the rotation axis. The energy spectrum in the ground and first excited states was analyzed and the exciton wave functions of these states were determined. It turned out that under the condition of intermediate confinement each exciton state is possible for definite geometry and size of the paraboloid of revolution. © Pleiades Publishing, Ltd. 2023. ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2023, Vol. 87, Suppl. 3, pp. S386–S389. Pleiades Publishing, Ltd., 2023.