标题： 时间依赖运动中受限伪简谐振子中的量子动力学 显示英文标题

标题： Quantum dynamics in confined pseudo-harmonic oscillator in a time-dependent moving

摘要： 在本工作中，我们给出了在移动边界条件下，受限伪谐波势的薛定谔方程的解析解，适用于任意角动量态。 结果表明，一个重要的量是核间距离比，它取决于埃玛科夫方程的解。 时变（TD）海森堡不确定积的最小值始终大于最小不确定积 h/2。 时变平均能量以封闭形式解析推导，相应的平均力和平均压强被定义。 此外，获得了六种选定双原子分子（CO、NO、ScH、CH、H2、N2）两种状态的时间相关函数。 发现其依赖于两个不同时间域的核间距离比。 在受限量子系统中，分子的时变生存概率和平均寿命被定义。 提供了量子相似性度量、差异性和量子相似性指数的表达式。 后者适用于一对分子。 所得结果与现有文献进行了比较，尽可能地。 据我们所知，这是首次在时变移动边界条件下对非谐波中心势的详细报告。 显示英文摘要

摘要： In this work, we present analytical solution of Schr\"odinger equation of confined pseudoharmonic potential in presence of a moving boundary condition, for an arbitrary angular momentum state. It turns out that an important quantity to probe the problem is internuclear distance ratio, which depends on the solution of Ermakov equation. The minimum value of time-dependent (TD) Heisenberg uncertainty product always remains greater than that of the minimum uncertainty product h/2. The TD average energy is derived analytically in a closed form and the corresponding average force and average pressure are defined. Moreover, time correlation function of two states for the case of six selected diatomic molecules (CO, NO, ScH, CH, H2, N2) is obtained. It is found to depend on internuclear distance ratio at two different time domains. The TD survival probability and average life-time of molecule in a confined quantum system are defined. Expressions are offered for quantum similarity measure, dissimilarity and quantum similarity index. The latter is given for a pair of molecules. The obtained results are compared with available literature, wherever possible. To our knowledge this is the first detailed report of a non-harmonic central potential in a TD moving boundary condition.