关键词: 量子摆, Mathieu函数, 概率密度

Abstract: 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.

Key words:  , quantum pendulum, Mathieu function, probability density