从整数阶角向Mathieu函数的特征值与特征函数出发，讨论了量子摆、谐振子和平面转子本征能量的区别与联系，分析了能级、摆面倾角和无量纲参数U0对概率密度分布的影响. 低能级的量子摆是非简并的，较高激发态能级的简并度为二，低能级量子摆的能量虽然与谐振子的接近，但概率密度的分布范围通常超过了经典单摆的情况，有多个因素影响倾斜量子摆的概率密度分布.

Based on the eigenvalues and eigenfunctions of the angular Mathieu function, we disscusse the energy differences and relationships among the inclined quantum pendulum, harmonic oscillator and plane rotor. The probability density distribution influenced by energy levels, inclination angles and dimensionless parameter U0 are also analyzed. The lower energy level of quantum pendulum is non-degenerate, but the degeneracy of the quantum pendulum at higher excited state is two. Although the quantum pendulum energy at lower energy level is close to that of the harmonic oscillator, the probability density distribution generally exceeds that of the classical pendulum. Several factors affect the probability density distribution of inclined quantum pendulum.