Quantum particle on the surface of a spherocylindrical capsule

Abstract

We study a spinless, nonrelativistic quantum particle confined to the curved surface of a homogeneous spherocylindrical capsule. We use Costa's method to formulate and solve the relevant Schr & ouml;dinger equation for this particle with only a confining potential, causing it to remain on the surface and free to move. We obtain the entire spectrum of the particle on the curved surface, demonstrating how the capsule's length-to-radius ratio influences the particle's eigenenergies and eigenfunctions.