含时库仑势和线性势的薛定谔方程的求解

Solution of Time-Dependent Coulomb Potential with Linear Potential

利用Burgan等人的时空变换方法对一类特殊形式的具有含时库仑势加线性项的薛定谔方程进行了分析和计算 ,并进一步讨论了更普遍形式的含时势V(r ,t) =- a0ξ12 r+ nk=1akrkξk2 + 1(其中 ξ =at2 +bt+c ,a0 ,a1,a2 ,… ,an,a ,b ,c是满足一定关系的常数 )

In this paper, we make use of the Burgan et al's method to derive the solution of the time dependent coulomb potential and linear potential with a special form, V(r,t)=-a 0ξ 12r+a 1rξ 32, (where ξ=at 2+bt+c, a 0, a 1, a,b,c are parameters with certain relations) and furthermore we discussed the wave function for V(r,t)=-a 0ξ 12r+nk=1 a kr kξ k2+1 (where a 0, a 1, ..., a n are constants), Meanwhile we analyzed the physical meaning of this special potential and the importance of the linear scaling factors C(t) in the study of repeated elastic reflections of a particle in an expanding spherical cavity.