Variational anisotropic model of Wannier excitons compared with fractional-dimensional space approach

Abstract

Binding energy of Wannier excitons in a quantum well of thickness $L$ is studied using two models: a two-parameter trial wave function and a fractional-dimensional space with dimension $2\leqslant \alpha \leqslant 3$. Since both models provide quantitative measures of the exciton spatial anisotropy as $L$ changes, we give physical arguments for a plausible definition of $\alpha =\alpha (L)$.