指数型变化有效质量的三维Schrdinger方程的解析解

Analytical solutions of the three-dimensional Schrdinger equation with an exponentially changing effective mass

对随径向坐标指数型变化的有效质量分布,通过坐标变换,得到了与Coulomb型势,Kratzer型势和无限深球方势阱三类势函数相联系的变质量三维Schr dinger方程的解析解,具体给出了这三类系统的能量本征值和本征函数的解析表达式.

For an effective mass distribution that is an exponential function of the radial coordinate, the analytical solutions of the three-dimensional Schrdinger equation are obtained by using the coordinate transformation method for the reference problems with Coulomb potential, Kratzer potential and spherically square potential well of infinite depth, respectively. The explicit analytical expressions for the energy eigenvalues and the corresponding eigenfunctions of the three systems are presented.