升降算符在一维谐振子能级讨论中的应用

Application of the raising and lowering operators in the discussion of one-dimensional harmonic oscillator energy levels

利用升降算符方法研究了一维谐振子的能级分布问题,给出了占有数表象升降算符â^(+)、â作用下的线性谐振子本征波函数的递推关系,最后利用升降算符讨论了线性谐振子本征波函数的代数表示形式.结果表明升降算符方法在研究谐振子的能级分布和本征波函数方面简洁易懂.

Using the raising and lowering operator method,the energy level distribution of a one-dimensional harmonic oscillator is studied,and the recurrence relation of the eigenwave function of a linear harmonic oscillator under the action of the elevating operator is given.Finally,the algebraic representation of the eigenwave function of a linear harmonic oscillator is discussed.The results show that the method is concise and easy to understand in studying the energy level distribution and eigenwave function of harmonic oscillator.