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.

中文翻译：

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平方根反平交叉量子二态模型

我们引入了一种新的无条件可解的水平交叉二态模型，该模型由恒定幅度的光场配置给出，其失谐是时间的平方根反函数。这是双汇合 Heun 模型的五个家族之一的成员。我们证明这是双汇合 Heun 类中唯一的非经典完全可解场配置，可根据 Hermite 函数的有限和来解。该模型的二态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 函数的不可约组合）。我们提出了一般的解决方案，