Description of electron transition in superlattice quantum well by ch-2x potential

An interaction potential with ch-2x form is introduced to describe the electron motion in superlattice quantum well, and in the frame of quantum mechanics, Schrodinger equation is transformed to the hypergeometric equation by this potential. The eigenvalue and the eigefunction of the system are calculated, and the distribution and the level number in quantum well are also discussed. As an example, the transition energy between two bands for material Ga1-xAlxAs-GaAs- Ga1-xAlxAs is calculated. It shows that the level number and the transition energy are related to the system parameters, such as the potential well depth, width etc. The photo-electric properties of superlattice materials can be controlled and regulated by regulating the system parameters.