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

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 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

So, we can look at other radial probability distributions of other wave functions that we talked about.

我们可以来看一看我们讨论过的,其它一些波函数的径向概率分布。

麻省理工公开课 - 化学原理课程节选

So again, we can think about the probability density in terms of squaring the wave function.

同样的，我们可以把,波函数平方考虑概率密度。

麻省理工公开课 - 化学原理课程节选

And in doing that, we'll also talk about the shapes of h atom wave functions, specifically the shapes of orbitals, and then radial probability distribution, which will make sense when we get to it.

为了这样做，我们要讲一讲，氢原子，波函数的形状，特别是轨道的形状，然后要讲到径向概率分布，当我们讲到它时，你们更能理解。

麻省理工公开课 - 化学原理课程节选

So if we're talking about probability density that's the wave function squared.

如果我们要讨论概率密度,这是波函数的平方。

麻省理工公开课 - 化学原理课程节选

That should make sense to us, because when we talk about a wave function, we're talking about a probability divided by a volume, because we're talking about a probability density.

因为我们说，波函数,是概率，除以体积,因为我们说的是，概率密度，如果我们用它。

麻省理工公开课 - 化学原理课程节选

So, what we can do to actually get a probability instead of a probability density that we're talking about is to take the wave function squared, which we know is probability density, and multiply it by the volume of that very, very thin spherical shell that we're talking about at distance r.

我们能得到一个概率,而不是概率密度的方法,就是取波函数的平方，也就是概率密度，然后把它乘以一个在ｒ处的,非常非常小的,壳层体积。

麻省理工公开课 - 化学原理课程节选

You can also have angular notes, and when we talk about an anglar node, what we're talking about is values of theta or values of phi at which the wave function, and therefore, the wave function squared, or the probability density are going to be equal to zero.

我们也可以有角向节点，当我们说道一个角向节点时，我们指的是在某个theta的值,或者phi的值的地方，波函数以及波函数的平方，或者概率密度等于零。

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