利用二次型理论精确求解双模耦合谐振子本征能级

Solving quadratic precision using mode coupling theory of intrinsic energy levels of harmonic oscillator

当两粒子在势场中运动时,由于两粒子之间存在相互作用,所以体系的哈密顿量必然会多出一项相互作用的耦合项.由于此耦合项的存在,使得体系本征能级的求解出现困难.本文主要介绍利用线性代数中的二次型定理,作一个线性变换消除其中的耦合项,并且此变换也不会引起本征能级的改变,也因此使其变成一个一般的二维势场问题,便可以精确求出其本征能级.

When two particles moving in the potential field, due to the interaction between two particles.Therefore,the Hamiltonian system is bound to a more interaction coupling. Since the existence of this coupling term system will be in demand when the intrinsic difficulty level,this paper is to introduce the use of linear algebra in the secondary type theorem for a linear transform in which the coupling term,and the nature of this transformation does not lead to changes in the intrinsic energy level,and therefore it becomes a normal two- dimensional potential field problem,we can precisely calculate its intrinsic energy level