Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.

我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。

麻省理工公开课 - 固态化学导论课程节选

We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.

我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。

麻省理工公开课 - 化学原理课程节选

But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.

波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。

麻省理工公开课 - 化学原理课程节选

Ever since this was first proposed, there has never been any observations that do not coincide with the idea, that did not match the fact that the probability density is equal to the wave function squared.

从未有，任何观测，与它相抵触,从没有过，波函数的平方不等于,概率密度的情况，关于马克思，波恩。

麻省理工公开课 - 化学原理课程节选

So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.

这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。

麻省理工公开课 - 化学原理课程节选

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

So the probability again, that's just the orbital squared, the wave function squared.

同样，概率密度，这就是轨道的平方，波函数的平方。

麻省理工公开课 - 化学原理课程节选

I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.

我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。

麻省理工公开课 - 化学原理课程节选

So, we can do that by using this equation, which is for s orbitals is going to be equal to dr 4 pi r squared times the wave function squared, d r.

用这个方程,对于s轨道，径向概率分布,4πr的平方,乘以波函数的平方,这很容易理解。

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

We call that a node, r and a node, more specifically, is any value of either r, the radius, or the two angles for 0 which the wave function, and that also means the wave function 0 squared or the probability density, is going to be equal to zero.

节点就是指对，于任何半径，或者，两个角度,波函数等于，这也意味着波函数的平方或者概率密度,等于，我们可以看到在1s轨道里。

麻省理工公开课 - 化学原理课程节选