Energy Spectrum of a constrained Quantum Particle and the Willmore Energy of the constraining Surface
arXiv:2302.06920 · doi:10.4310/ATMP.2023.v27.n8.a3.
Abstract
Geometric and topological bounds are obtained for the first energy level gap of a particle constrained to move on a compact surface in 3-space. Moreover, geometric properties are found which allows for stationary and uniformly distributed wave functions to exist on the surface.