Recently Gnatenko et al. (J Phys Stud 21:4002, 2017) have treated the two-body problem with harmonic oscillator interaction in noncommutative phase space. According to the path integral formulation, we generalize this process by adding the coupling potentials (\(\kappa {\mathbf {P}} ^{\left( a\right) }\cdot {\mathbf {P}}^{\left( b\right) }\) and \({\tilde{\kappa }} {\mathbf {X}}^{\left( a\right) }\cdot {\mathbf {X}}^{\left( b\right) }\)) together with a Harmonic oscillator interaction in noncommutative phase space. Moreover, in order to convert this problem into a one-particle system, we have added a third condition along with what this paper provided. As well as, when \( \kappa \) and \({\tilde{\kappa }}\) equal to zero exact expressions for the energy levels of a two-particle system with harmonic oscillator interaction in noncommutative phase space have been found.

最近，Gnatenko等。（J Phys Stud 21：4002，2017）用非交换相空间中的谐振子相互作用来解决两体问题。根据路径积分公式，我们通过添加耦合电势（\（\ kappa {\ mathbf {P}} ^ {\ left（a \ right）} \ cdot {\ mathbf {P}} ^ {\ left（b \ right）} \）和\（{\ tilde {\ kappa}} {\ mathbf {X}} ^ {\ left（a \ right）} \ cdot {\ mathbf {X}} ^ {\ left （b \ right）} \））和非交换相空间中的谐波振荡器相互作用。此外，为了将此问题转换为单粒子系统，我们在本文提供的基础上增加了第三个条件。以及，当\（\ kappa \）和\（{\ tilde {\ kappa}} \）时 对于非交换相空间中具有谐振子相互作用的两粒子系统的能级，发现等于零的精确表达式。