The quantum bouncer by the path integral method
The quantum bouncer by the path integral method
复制标题
路径积分法的量子弹跳器
DOI：
10.1119/1.16673
复制
发表时间：
1991
影响因子：
0.9
通讯作者：
T. Szeredi
中科院分区：
文献类型：
--
作者：
D. A. Goodings;T. Szeredi
The path integral formulation of quantum mechanics in the semiclassical or WKB approximation provides a physically intuitive way of relating a classical system to its quantum analog. A fruitful way of studying quantum chaos is based upon applying the Gutzwiller periodic orbit sum rule, a result derived by the path integral method in the WKB approximation. This provides some motivation for learning about path integral techniques. In this paper a pedagogical example of the path integral formalism is presented in the hope of conveying the basic physical and mathematical concepts. The ‘‘quantum bouncer’’ is studied—the quantum version of a particle moving in one dimension above a perfectly reflecting surface while subject to a constant force directed toward the surface. The classical counterpart of this system is a ball bouncing on a floor in a constant gravitational field, collisions with the floor being assumed to be elastic. Path integration is used to derive the energy eigenvalues and eigenfunctions of th...
