广义n维耦合谐振子体系的代数解法

摘要

Using the quadratic form theory, we achieve the decoupling of systematic Hamiltonian of generalization of n-dimensional coupled harmonic oscillators and derive the diagonalized Hamiltonian by three linear transformations with keeping the commutation relations unchanged. The energy eigenvalue and the eigenfunction of the system are also obtained.%利用二次型理论,通过三次保对易线性变换,实现了广义n维耦合谐振子体系哈密顿量的退耦合,得到了体系对角化后的哈密顿量,并给出了体系的能量本征值和本征函数.