摘要：对微观粒子量子谐振动的量子尺寸效应进行表征,给出量子谐振子精确的量子哈密顿量,建立适合量子谐振子特性的量子算符代数理论。根据创新的量子谐振子的量子算符代数理论,得到量子谐振子的能量关系。结果表明:量子谐振子的能量为常量,其值与时间量子数无关,不同时间量子态量子谐振子的能量都相同。

关键词：微观粒子；量子谐振子；哈密顿量

Abstract：The exact guantum Hamiltinian for quantum harmonic oscillator was given. The quantum operator algebralc theory was porposed first to suit the character of the quantum harmonic oscillator. Based on the quantum operator algebraic theory for quantum harmonic oscollatoy， the energy relationship of the quantum harmonic oscillator were obtained. The results showed that the quantum harmonic oscillator′s energy was a constant，which had nothing to do with the time quantum number. 

Keywords： microscopic particle； quantum harmonic oscillator； Hamiltonian