Time-independent approximations for time-dependent optical potentials
Time-independent approximations for time-dependent optical potentials
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DOI：
10.1140/epjp/s13360-020-00143-y
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
A. Fring;Rebecca Tenney
中科院分区：
文献类型：
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作者：
A. Fring;Rebecca Tenney
我们探索了修改Lewis-Riesenfeld不变量方法的可能性，该方法最初是为了求含时量子力学系统的精确解，在这种情况下，可以构造精确的不变量，但随后得到的与时间无关的本征值系统不是精确可解的。我们建议以一种近似的方式执行这一步骤，例如使用标准的与时间无关的微扰理论或WKB近似，然后将所得到的近似表达式反馈到依赖于时间的格式中。我们通过比较两类显式含时光学势的精确可解解和微扰第二步解来说明这种方法的质量。
We explore the possibility of modifying the Lewis–Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed, but the subsequently resulting time-independent eigenvalue system is not solvable exactly. We propose to carry out this step in an approximate fashion, such as employing standard time-independent perturbation theory or the WKB approximation, and subsequently feeding the resulting approximated expressions back into the time-dependent scheme. We illustrate the quality of this approach by contrasting an exactly solvable solution to one obtained with a perturbatively carried out second step for two types of explicitly time-dependent optical potentials.