一类变质量变频谐振子的波函数

对于质量和频率随时间变化的谐振子，当频率ω=ω（t），质量m=m（0）ω（0）/ω（t）exp2c∫0^t ω（t）dt]时，通过替换薛定谔方程中的变量，可用变量分离的方法求解薛定谔方程；然后根据常量c的取值不同，分别求出了c^2〈1、c^2=1和c^2〉1时的波函数．结果表明：若c^2〈1，当｜x｜→∞时，波函数趋近于零；若c^2≥1，当｜x｜→∞时，波函数并不趋近于零．最后，给出了这类变质量变频谐振子的几种特例，其中之一类似于阻尼谐振子．

The Wave Functions for a Time-dependent Harmonic Oscillator

The time-dependent Schrodinger equation for the harmonic oscillator with time-dependent frequency ω=ω（t） and mass m=m（0）ω（0）/ω（t）exp2c∫0^t ω（t）dt] can be solved by means of simple transformation and separationof variables. The wave functions are obtained for c^2 〈 1, c^2 = 1 and c^2 〉 1, respectively. When ｜x｜→∞, the wave function for c2^ 〈 1 tends to zero but it is not so for c^2 ≥ 1. Finally, some special cases are given for the time-dependent harmonic oscillator and one of them is similar to a damped harmonic oscillator.