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But a real key in looking at these plots is where we, in fact, did go through zero and have this zero probability density.
是我们经历这些零值,而且有这些零概率密度,我们把它叫做节点。
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And so, the radial probability density at the nucleus is going to be zero, even though we know the probability density at the nucleus is very high, that's actually where is the highest.
所以径向概率密度,在核子处等于零，虽然我们知道在，核子处概率密度很大,实际上在这里是最大的，这是因为。
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Conversely, if there was probability 1 that the other guy is going to choose Right, and I choose Up, then I get 0.
相反,如果对手,选择右的概率为1,并且我选的是上,那我的收益为零
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If you're relentlessly selfish and calculating you would say, the chances that I decide the election are zero, so I'm just not going to bother.
如果你唯利是图,精于算计,你会说,我的投票能够决定选举的概率是零,所以我根本无需投票
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Anywhere where that's the case we're going to have no probability density of finding an electron.
这时面内任何地方,找到电子的概率密度都是零。
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So, the wave function at all of these points in this plane is equal to zero, so therefore, also the wave function squared is going to be equal to zero.
因此这里的,波函数平方也等于零，如果我们说在这整个平面上,任何地方找到一个ｐ电子的概率都是零。
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The answer is, in fact, there is zero, absolutely zero probability of finding a electron here.
实际上它在这里是为零的，在这里找到电子的概率严格等于零。
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The other thing that we looked at, which I want to stress again and I'll stress it as many times as I can fit it into lecture, because this is something that confuses students when they're trying to identify, for example, different nodes or areas of no probability.
另外一个我们要考虑的事情，我想再强调一次,而且我以后会在课上强调很多次，因为它很容易让人混淆,这就是当你们在确认，节点或者零概率点时候。
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That's different when you have continuous values-- you don't have P because it's always zero.
和离散型随机变量的分布不同的是,连续型随机变量的分布中,某一点的概率值始终是零
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So, if we say that in this entire plane we have zero probability of finding a p electron anywhere in the plane, the plane goes directly through the nucleus in every case but a p orbital, so what we can also say is that there is zero probability of finding a p electron at the nucleus.
而只要是ｐ轨道,这个平面都直接，穿过原子核，那么我们,可以说在原子核上,找到一个ｐ电子的概率为零。
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So, that can be a little bit confusing for us to think about, and when it's a very good question you might, in fact, say well, maybe there's not zero probability here, maybe it's just this teeny, teeny, tiny number, and in fact, sometimes an electron can get through, it's just very low probability so that's why we never really see it.
这想起来有点令人困惑，你们可能会说也许，这里的概率并不是严格的为零，而是非常非常小，所以有时电子就可以穿过去，这是个,很好的想法。
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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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It looks like we hit zero, but we actually don't remember that we never go all the way to zero, so there's these little points if we were to look really carefully at an accurate probability density plot, And then, for example, how many nodes do we have in the 3 s orbital?
但其实没有，记住，我们永远不会到零,如果我们，在概率密度图上,非常细致的看这些点的话,它永远不会到零，在3s轨道里，有多少个点呢？，2个，正确？
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