Harmonic oscillator with potential barriers-exact solutions and perturbative treatments
Harmonic oscillator with potential barriers-exact solutions and perturbative treatments
复制标题
具有潜在障碍的谐波振荡器-精确解和微扰处理
DOI：
10.1088/0305-4470/16/8/010
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
Y. C. Lee
中科院分区：
文献类型：
--
作者：
W. Mei;Y. C. Lee
精确地解决了两个特殊的势阱问题，一个是具有有限势阶跃的半空间谐振子，另一个是具有无限壁的全空间谐振子。这些研究的目的是调查的限制情况下，（i）在第一种情况下的有限位阶是非常高的能量本征值相比，低的状态和（ii）在第二种情况下的无限位壁是在一个很大的距离，从原点的低的状态的波函数的振幅为零的小。数值结果与Lee和Mei提出的摄动格式的解析表达式进行了比较。取得了很好的协议。一般的影响和应用进行了讨论。
Two specific potential-well problems have been solved exactly, firstly, a half-space harmonic oscillator with a finite-potential step and secondly, a full-space harmonic oscillator with an infinite wall located at a finite distance from the origin. The purpose of these studies is to investigate the limiting situations when (i) the finite-potential step in the first case is very high compared with the energy eigenvalues of the low-lying states and (ii) the infinite-potential wall in the second case is at a great distance from the origin where the amplitudes of the wavefunctions of the low-lying states are vanishingly small. The numerical results have been compared with the analytical expressions obtained from the perturbation schemes devised by Lee and Mei. Excellent agreements are obtained. General implications and applications are also discussed.