Combination of Hartree and Ritz approaches for problem of excitons in semiconductor quantum wells. Additional exciton states

A combination of Hartree and Ritz approaches is applied to the problem of exciton confined in a semiconductor quantum well (QW). The multiplicative representation of exciton wave function is shown to describe satisfactorily the exciton states in the QWs of arbitrary width if electron and hole confinement components are found from the Hartree-like self-consistent equations. The method is illustrated by calculations of ground exciton states in single-band approximation. The validity of other approximations widely applied in the present literature is also discussed. The maximal error of exciton binding energy determination in the model is obtained. The method is applied for the analysis of additional exciton states that are absent without electron–hole Coulomb interaction. Asymmetry of the QW potential can be responsible for the manifestation of optical transitions associated with these additional states with quantum numbers of different parities. The relatively simple procedure developed here can be applied to systems with weak or even absent carrier localization by quantum-well potential (e.g. excitons in type II heterostructures).