作为精确可解模型的分子非对称刚性转子哈密顿量
The molecular asymmetric rigid rotor Hamiltonian as an exactly solvable model
摘要：
旋转群的表示可以通过施温格将角动量态转录到有效二维振子的态上，用第二量子化语言来表达。在分子非对称刚性转子的情况下，通过投影到刚体旋转的状态空间上，标准Ray Hamilton算子$H(1,κ,-1)$（具有非对称参数$1 \ge κ\ge -1$）在相关动力学$su(1,1)$代数的生成元中变成二次多项式。指出$H(1,κ,-1)$在Gaudin算子中实际上是二次的，Gaudin算子是由一个相关的$su_q(1,1)$ Yang-Baxter代数的拟经典极限所产生的.因此，一般的非对称刚性转子哈密顿量是一个精确可解的模型。这一事实对光谱的结构以及模型的本征态和关联函数有重要的意义。
英文摘要：
Representations of the rotation group may be formulated in second-quantised language via Schwinger's transcription of angular momentum states onto states of an effective two-dimensional oscillator. In the case of the molecular asymmetric rigid rotor, by projecting onto the state space of rigid body rotations, the standard Ray Hamiltonian $H(1,κ,-1)$ (with asymmetry parameter $1 \ge κ\ge -1$), becomes a quadratic polynomial in the generators of the associated dynamical $su(1,1)$ algebra. We point out that $H(1,κ,-1)$ is in fact quadratic in the Gaudin operators arising from the quasiclassical limit of an associated $su_q(1,1)$ Yang-Baxter algebra. The general asymmetric rigid rotor Hamiltonian is thus an exactly solvable model. This fact has important implications for the structure of the spectrum, as well as for the eigenstates and correlation functions of the model.
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