论文标题
逆平方根级别的量子两态模型
Inverse square root level-crossing quantum two-state model
论文作者
论文摘要
我们引入了一种由恒定振幅光场配置给出的新的无条件可解决水平的两态模型，该模型对此是时间的反向平方根函数。这是五个双重共鸣模型的家庭之一。我们证明，这是双重共鸣类中唯一的非经典溶解场配置，可以根据Hermite函数的有限总和来解决。该模型的两国问题的一般解决方案是根据移位和缩放参数的四个Hermite函数编写的（两个基本解决方案中的每一个都呈现了两个Hermite函数的不可约合组合）。我们提出了一般解决方案，以更熟悉的物理量来重写，并分析量子系统的时间动力学，但通过这种配置的激光场激发了激发。
We introduce a new unconditionally solvable level-crossing two-state model given by a constant-amplitude optical field configuration for which the detuning is an inverse-square-root function of time. This is a member of one of the five families of bi-confluent Heun models. We prove that this is the only non-classical exactly solvable field configuration among the bi-confluent Heun classes, solvable in terms of finite sums of the Hermite functions. The general solution of the two-state problem for this model is written in terms of four Hermite functions of a shifted and scaled argument (each of the two fundamental solutions presents an irreducible combination of two Hermite functions). We present the general solution, rewrite it in terms of more familiar physical quantities and analyze the time dynamics of a quantum system subject to excitation by a laser field of this configuration.
