Abstract: Based on the basic knowledge of statistical physics and the calculation process of diatomic ideal gas heat capacity, the linear harmonic oscillator and space rotor model are studied. The partition function of particles at room/cool temperature and high temperature is calculated. At room temperature, the particle partition function is $z=\frac{1}{N!}\frac{T}{T_{r}}e^{-\beta \frac{1}{2}\hbar\omega}$. At high temperature, the particle partition function is $z=\frac{1}{N!}\frac{T}{T_{r}}(e^{-\beta \frac{1}{2}\hbar\omega}+e^{-\beta \frac{3}{2}\hbar\omega}+e^{-\beta \frac{5}{2}\hbar\omega}+...)$. With the partition function, we can calculate any required physical quantity, such as energy, pressure and entropy.

Key words: linear harmonic oscillator, space rotor, coupling between rotation and vibration, partition function