利用二次型理论精确求解双模双耦合谐振子的能谱

Accurately Solve the Energy Eigenvalue of the 2D Double Coupling Harmonic Oscillator by Means of Quadratic Form Theory

利用二次型理论构造一个幺正矩阵进行坐标变换,将质量和频率均不相同的双模双耦合谐振子体系的哈密顿量对角化,得出一般双模双耦合谐振子体系能谱的精确解,同时提供了一种解决该类问题的一般数学方法.

Structuring a unitary matrix for transformation of coordinates by means of quadratic form theory,we transform Hamiltonian of the 2D double coupling harmonic oscillator with both different mass and different frequency into diagonalmatrix,attain the accurate answer of the energy eigenvalue of the 2D double coupling harmonic oscillator and at the same time offer a general mathematic method for solving this kind of problems.