General solution of Schrödinger equation and electron transition in superlattice multi-quantum well

Abstract

Supposing that the quantum well of a superlattice is a periodic potential well of an arbitrary shape, the motion problem of electrons in the superlattice can be reduced into the motion in a periodic field. From the Schrödinger equation and its general solution, the dispersion equation of the system can be derived using Bloch theory and the transfer matrix method in the framework of quantum mechanics; and the electronic transitions of the multi-quantum well for the superlattice can be discussed in parabolic approximation. Results show that the radiation energy is located at the infrared, far infrared or terahertz band.