利用二次型求解n模耦合谐振子能量本征值精确解

Solving energy eigenvalue of n module coupling harmonic oscillators by virtue of quadratic form

利用二次型理论构造一个幺正矩阵进行坐标和动量变换,把n模动量耦合谐振子体系的哈密顿量化为标准的二次型,进而得到n模动量耦合谐振子体系的能量本征值.对n模坐标耦合的情况也进行了类似求解,并提供了解决该类问题的一般数学方法.

A unitary matrix is constructed by virtue of quadratic form theory for coordinates and momentums transformation. The Hamihonian of the n-D coupling harmonic oscillators is diagonalized by means of the transfor- mation. The exact solution of energy spectrum of n-D coupling quantum harmonic oscillator is given. It also offers a general mathematic method solving problems of this kind.