Usual interaction potential is the squared potential well to describe the motion behaviour of a hole in the single quantum well. The new interaction potential with ch^－2x form is assumed. In the frame of quantum mechanics,Schr?dinger equation to describe the particle motion is reduced to the hypergeometric equatin by this potential. The eigenvalue and the eigefunction problem of the Schr?dinger equation are transformed to the eigenvalue and the eigefunction problem of the hypergeometric equation. The eigenvalue and the eigefunction of the system are calculated,and the distribution and number of level in quantum well are discussed. As example,the level and the transition of a hole in the single quantum well for material Ga_1-xAl_xAs-GaAs-Ga1-xAl_xAs are calculated. It shows that coincidence between the theory and the experiment is improved futher.