An analytical method is developed to study the two-mode quantum Rabi model. For certain specific parameter conditions, especially for the resonant conditions, we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies. It is shown that there exist new types of the exact energies which do not correspond to the level-crossings. Our analytical method may find applications in some related models.

中文翻译：

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两模量子拉比模型的精确解

开发了一种分析方法来研究双模量子拉比模型。对于某些特定的参数条件，特别是对于共振条件，我们获得了本征函数和相关能量的无限数量的精确解。结果表明，存在新的精确能量类型，它们不对应于平交路口。我们的分析方法可能会在某些相关模型中找到应用。