Quantum aspects of a moving neutral particle possessing a magnetic quadrupole moment that interacts with an axial electric field in the presence of a two-dimensional harmonic oscillator are investigated in the background of noncommutative space. The energy levels of bound states and the corresponding wave functions are obtained using analytical method. It is shown that the effects of space noncommutativity and harmonic oscillator modify the spectrum of energy and remove the degeneracy of the Landau-type system. Furthermore, solutions of bound states as well as the associated wave functions are also investigated in the context of noncommutative space when the magnetic quadrupole moment interacts with a radial magnetic field under the two-dimensional harmonic oscillator using the Frobenius method. As quantum effect, it is shown that the harmonic oscillator frequency becomes determined by the quantum numbers of the system and by the noncommutativity parameter \(\theta \). In order to show the effects of space noncommutativity on the system, some figures are also presented.

在非对易空间的背景下，研究了具有磁性四极矩的移动中性粒子在二维谐振子存在的情况下与轴向电场相互作用的量子方面。使用解析方法获得束缚态的能级和相应的波函数。结果表明，空间非对易性和谐振子的影响改变了能量谱，消除了朗道型系统的简并性。此外，当磁四极矩与二维谐振子下的径向磁场相互作用时，还使用 ​​Frobenius 方法在非对易空间的背景下研究了束缚态的解以及相关的波函数。作为量子效应，\(\theta \)。为了显示空间非对易性对系统的影响，还给出了一些图形。