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

So this line represents the expected payoff of shooting to the middle as a function of the probability that the goal keeper dives to the right.

这条线表示从中路射门时罚球者的收益,是门将扑向右路概率的一个函数

耶鲁公开课 - 博弈论课程节选

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 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

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

And here's my green line representing my expected payoff as the shooter, from shooting to the right, as a function of the probability that the goalie dives to the right.

这条绿线表示作为一个罚球球员,我从右路射门的收益,是门将扑向右路概率的一个函数

耶鲁公开课 - 博弈论课程节选

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, 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 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

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

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

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