Effects of hydrostatic strain on eigenstates of Möbius strips

In this paper we theoretically investigate the allowed energies and associate wave-functions for Möbius strips with varying thicknesses. We show that the induced strain in fabricating these Möbius strips will have an pronounced impact on the energies and wave-functions for thick strips, while for thin strips the impact of strain is negligible. We furthermore, show that a simpler strain free approximate theory base on differential geometry is in excellent agreement with detailed finite element calculations.