耦合谐振子是量子光学中的重要问题之一,许多实际物理问题的解决都依赖于耦合谐振子的模型,因此研究耦合谐振子求解的简便方法显得十分必要.运用数学上二次型正交化理论构造了一个形式上的变换矩阵,使既有坐标耦合又有动量耦合的各向异性n维耦合谐振子的Hamiltonian对角化,求出了其本征值.并应用此方法求解了三维耦合谐振子的本征值,验证了该方法的正确性.由于该方法不需要求出变换矩阵的具体形式,使得运用此方法求解具有对称形式的Hamiltonian的本征值问题变得简单、易计算出结果,该方法更具有普遍性,是一种十分有效的代数方法.
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