And when we take the wave function and square it, that's going to be equal to the probability density of finding an electron at some point in your atom.

当我们把波函数平方时，就等于在某处,找到一个电子的概率密度。

麻省理工公开课 - 化学原理课程节选

So again if we look at this in terms of its physical interpretation or probability density, what we need to do is square the wave function.

如果我们从物理意义或者,概率密度的角度来看这个问题，我们需要把波函数平方。

麻省理工公开课 - 化学原理课程节选

to do sqrt, or square root-- no, I'm going to square root use sqrt, that's the name I'm using here-- square root a hundred different places in some piece of code. Without function, I'd have to copy that piece of code everywhere.

让我做一下准备,想象一下我要调用sqrt或者-,不，我会调用sqrt函数,这是我在这里用的名字，我得把这段代码到处复制。

麻省理工公开课 - 计算机科学及编程导论课程节选

Now, I hope you guys know that much calculus, that when you take a derivative of a function of a function, namely v square over 2 is a function of v, and v itself is a function of t, then the rule for taking the derivative is first take the v derivative of this object, then take the d by dt of t, which is this one.

我希望你们了解更多的微积分知识,当你对复合函数求导时,也就是说v^/2是关于v的函数,而v本身是关于t的函数,求导的法则应该是,第一步是这一部分对v求导,然后v再对t求导,得到这一部分

耶鲁公开课 - 基础物理课程节选

So, at this place where it hits zero, 0 that means that the square of the wave function is also going to be zero, right.

它达到0的地方，这意味着波函数的，平方也是,如果我们看概率密度图。

麻省理工公开课 - 化学原理课程节选

And what here is just a graph of the 1 s wave function going across some radius defined this way, and you can see that the probability - well, this is the wave function, so we would have to square it and think about the probability.

这里是,1s波函数,沿这个方向的图，你们可以看到概率,这是波函数，所以我们可以把它平方,并想成是概率。

麻省理工公开课 - 化学原理课程节选