浅议共轭薛定谔方程及其物理量算符

Discussion on the conjugated Schrodinger equation and its physical quantity operator

状态函数一般是复函数,其物理意义的解释依然是个开放的话题。德国物理学家Born曾把粒子状态函数的模平方与粒子出现的概率对应起来。但除此之外,几乎没有更加深刻的对状态函数物理意义的解释。通过对薛定谔方程进行简单变换,可得与其共轭的波动方程。采用对比法研究了两个薛定谔方程的性质,给出了二者本征函数、物理量算符间的关系。结合密度泛函理论得出,两个方程在描述物理性质方面无本质差别,且含时波函数必是非实数波函数的结论。

Generally, the state function is a complex function, whose physical meaning still deserve more investigation. The German physicist Born had ever pointed out that, the modular square of the state function represent the density function of probability. However, there is hardly any more profound interpretation on the physical meaning of the state function. For the Schrodinger wave equation, by a simple mathematical transformation, a conjugated wave equation is obtained. The mathematical property of the two Schrodinger wave equations is compared, the relation between two sets of eigenfunction and physical operator is investigated. According to density function theory, two wave equations have no essential distinction in state description, and the time-dependent state function should be a non-real function.