An approximate analytical solution of the Schrödinger equation is obtained to represent the rotational–vibrational (ro-vibrating) motion of a diatomic molecule. The ro-vibrating energy states arise from a systematical solution of the Schrödinger equation for an empirical potential (EP) V ±(r) = D e {1 − (ɛ/δ)[coth (ηr)]±1/1 − (ɛ/δ)}2 are determined by means of a mathematical method so-called the Nikiforov–Uvarov (NU). The effect of the potential parameters on the ro-vibrating energy states is discussed in several values of the vibrational and rotational quantum numbers. Moreover, the validity of the method is tested with previous models called the semiclassical (SC) procedure and the quantum mechanical (QM) method. The obtained results are applied to the molecules H2 and Ar2.
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机译:获得了薛定ding方程的近似解析解,以表示双原子分子的旋转振动(转子振动)运动。旋转振动能级来自系统对Schrödinger方程的经验势(EP)V ± sub>(r)= D e sub> {1-(ɛ/ δ)[coth(ηr)] ±1 sup> / 1-(ɛ/δ)} 2 sup>是通过称为Nikiforov–Uvarov( NU)。在振动和旋转量子数的几个值中讨论了势参数对旋转振动能量状态的影响。此外,该方法的有效性已通过先前称为半经典(SC)程序和量子力学(QM)方法的模型进行了测试。所得结果应用于分子H 2 sub>和Ar 2 sub>。
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