The special structure of superlattice leads to strong interest from 1970’s

because it has the particular photo-electric characteristics.Along the development of the film technique

the component and the thinckness for the superlattice material can be controlled artificially

then gap engineering and doping engineering are formed.The well width can be regulated by means of controlling the thinckness of the film for the superlattice material;the well deep can be regulated also by means of controlling the component for the superlattice material.If the barrier layer of the multi-quantum well or superlattice was slight enough

the small size effect must consider.Of course

if the barrier layer of the multi-quantum well or superlattice was think enough

to such an extent as to the interaction between quantum wells can be neglected

the superlattice can be regarded as the single repeat of the single quantum well

then problem of multi-quantum well reduced to the problem of the single quantum well.Usual interaction potential is the squared potential well to describe the motion behaviour of an electron in the single quantum well.The new interaction potential with tan

2

x form is leaded.In the frame of quantum mechanics

equation to describe the particle motion is reduced to the hypergeometric equation by this potential.The energy eigenvalue and the eigenfunction problem of the equation are transformed to the eigenvalue and the eigenfunction problem of the hypergeometric equation.The eigenvalue and the eigenfunction of the system are calculated

and the distribution of level in quantum well are discussed.As an example

the level and the transition of an electron in the single quantum well for material Ga

1-x

Al

x

As-GaAs-Ga

1-x

Al

x

As are calculated.It shows that coincidence between the theory and the experiment is improved futher.