一般幂指数中心势作用下的波包回归和部分回归

利用WKB近似和自关联函数方法,我们研究了一般幂指数中心势V(r)=γrk (-20)作用下波包的回归和部分回归.对于排斥势(γ>0, k>0), 势是一长程势,量子化能级结构中只有一个量子数,波包的回归结构和一维幂指数势的情况类似.这一结果表明能级结构相同的体系具有相同的波包回归结构.对于吸引势,能级结构中有两个量子数, 当 k取不同的值时,波包的回归结构不同.对于库仑吸引势,波包回归和部分回归出现;但是对于其它的k值, 经过一段时间后,波包出现坍塌.本文的研究对于探讨里德堡原子和分子中电子运动的经典极限提供了一个新的方法.

Wave packet revivals and fractional revivals in the general power law central potential

Using the WKB approximation and the autocorrelation function approach, we study the wave packet revival and fractional revival in the general power law central potential V(r)=rk (-20). For the repulsive potential ( >0, k>0), the potential is a long-ranged one. There is only one quantized number in its quantized energy and the structures of its wave packet revivals are similar to the case of the one-dimensional power-law potential. These results show that systems with identical energy level structures exhibit similar wave packet revival patterns. As for the attractive potential, there are two quantum numbers in the energy, therefore, for different values of k, the structures of the wave packet revivals are not nearly the same. For the special case of the Coulomb attractive potential, the revivals and fractional revivals of the wave packet appear. While for other values of k, the wave packet collapses after a period of time. The study in this paper offers a new method to investigate the classical limit of the motion of electrons in Rydberg atoms or molecules.