This cartoon shows the probability density function of 1s.

下面这个动画表示了,数1s轨道的概率密度函数。

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We can graph out what this is where we're graphing the radial probability density as a function of the radius.

我们可以，画出它来,这是径向概率密度,作为半径的一个函数图。

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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。

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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。

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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。

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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。

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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。

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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 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。

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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。

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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。

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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。

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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。

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