量子谐振子与经典谐振子的比较

Comparison of quantum harmonic oscillator and classical harmonic oscillator

在Heisenberg表象,通过引入升降算符求解了量子谐振子,计算了任意初态情况下坐标、动量、动能、势能和哈密顿量的期望值,并同经典谐振子的相应力学量进行了比较,得出了量子谐振子只能在一定条件下趋近于经典谐振子而不可能等同。

The harmonic oscillator was solved in the Heisenberg representation by introducing raising operator and lowering operator. The expectation values of coordinates, momentum, kinetic energy, the potential energy and Hamilton quantity were calculated under any initial state. And these expectation values were comlzared with corresponding mechanical quantity of the classical harmonic oscillator. It is concluded that the quantum harmonic oscillator tends to the classical limit only in certain condition, but they are not identical.