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.
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