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So, for example, we have this average level, and then it can go high where we have the peak, or it can go very low. We can also discuss sound waves, so again it's just the periodic variation of some property -- in this case we're talking about density, so we have high density areas and low density areas.
例如这是平均位置，在峰的位置水位高，在谷水位低，我们也可以,讨论声波它也是某种,量的周期变化，在这里我们,讨论的是密度,我们有高密度区和低密度区。
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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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Think of anything else with the density goes down when it freezes, and think about where we would be if that wasn't the case.
想想有没有其他的物质,在降温时密度会变大，再想想如果不是这种情况,我们将会怎么样。
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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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So, instead of having the periodic variation of water, or the periodic variation of air density here we're talking about an electric field.
不像水或者空气密度的,周期变化，我们这里,讨论的是电场。
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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。
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When we were talking about constructive interference, we had more electron density in between the 2 nuclei.
当我们讨论相长干涉的时候，在两个原子核之间有更多的电子密度。
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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 we talked about radial nodes when we're doing these radial probability density diagrams here.
我们画这些径向概率分布图的时候,讨论过径向节点。
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This is the probability density map, so we're talking about the square here.
这是它的概率密度图，我们看的是平方。
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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, when we're talking about the idea of electronegativity, essentially what we're talking about is the ability for an atom to attract electron density from another atom.
那么，当我们在讨论电负性这一概念的时候，本质上我们讨论的是一个原子的吸引能力,用来吸引另一个原子的电子密度的。
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6 It's got a density of about 1.76 at room temperature.
在室温下密度是1。
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let's think about probability density.
让我们来考虑概率密度。
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So, this is about a quarter of the density of steel.
所以镁的密度是贴的四分之一。
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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。
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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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And one common way to think about it, is to think about the value of r, or the radius, below which 90% of that electron density is going to be contained.
而通常的想法，是想象，r，的值，也就是半径的值，即有百分之九十的电子密度,都落在这个范围之内。
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a perfectly spherical shell dr at some distance, thickness, d r, dr we talk about it as 4 pi r squared d r, so we just multiply that by the probability density.
在某个地方的完美球型壳层,厚度，我们把它叫做4πr平方，我们仅仅是把它,乘以概率密度。
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So if we talk about the probability density and we write that in, it's going to be sigma 1 s star squared, 1sb so now we're talking about 1 s a minus 1 s b, all of that being squared.
如果我们讨论概率密度，而且我们把它写出来，它等于sigma1s星的平方，现在我们说的是1sa减去，这整体再平方。
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