中文摘要：

用超对称性量子力学和形状不变势,求解了12种可以在柱坐标下分离变量的非中心势,并给出了其能量本征值以及本征函数的解析形式.利用此结果以及已经建立的一维含时超对称量子力学的结果,将含时超对称量子力学推广到高维情况,提出了一种可以用来精确求解含时非中心势的理论方法,并利用此方法求解了6种可以在球坐标下分离变量的含时非中心势和另外6种可以在柱坐标下分离变量的含时非中心势,同时给出了其本征值与相应的本征函数的解析形式.

英文摘要：

Twelve noncentral but separable potentials in cylindrical coordinates are solved by using supersymmetry algebra and shape invariant potential, the energy eigenvalues and the eigenfunctions are given analytically. Based on it and the results of one-dimensional time-dependent supersymmetric quantum mechanics, the time-dependent supersymmetry is generalized to higher dimensions, a method for solving non- central but separable time-dependent potentials is formalized, six noncentral but separable time-dependent potentials in spherical coordinates have been solved, and other six ones in cylindrical coordinates have been worked out as well, the analytical expressions of the enery-eigenvalues and the wavefunctions are given explicitely.