线性谐振子的算符理论

The Operator Theory of Linear Resonance

谐振子在量子力学中占有重要的地位.在一般量子力学教材中处理线性谐振子问题都是采用在坐标表象中求解定态薛定谔方程的方法,这种解法繁复而冗长.而采用海森堡矩阵力学的方法,在定态情况下只需知道一个体系的哈密顿算符^H和量子化条件[^Xα,^Pβ]=iδαβ,便可确定它的全部性质.这种方法为在一般情况下从经典力学过渡到量子力学提供了一个标准程序即正则量子化.

Though the resonance in the quantum mechanics is very important the linear resonance in the text is usuanlly treated with the stationary state E Schrodinger equation in coordinate ideal for answer This procedure is complicated and verbose If we use the Heisenberg's matrix mechanics way and only know one system of Hamilton operator and quantizing condition α, β]=iδ αβ its all properties can be determined In this way it can supply a standard procedure from classic mechanics to quantum mechanics and it not only has universal signficance but also can be extended and sued easily =iδ αβ its all properties can be determined In this way it can supply a standard procedure from classic mechanics to quantum mechanics and it not only has universal signficance but also can be extended and sued easily