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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。
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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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In fact, you'll find the probability of this happening 3% is only about 3 percent, of it happening just by accident.
实际上你会发现,出现这种情况的概率是，所以说他们的实验结果完全是偶然的。
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If you had a course in probability and statistics, then you'll find it easy to follow, but it's self-contained again.
如果你们学过统计学或者概率论,你们会比较容易理解,也需要你们独立学习
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So the probability is 0 of the other guy choosing Left is, the same as, let's try it again.
同样的如果对手选左的概率是0,那也就是说,重新来
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So in all probability, anyone who was associated with the hated occupying regime would be treated poorly It all seems to fit.
因此极有可能，任何一个人,与当权政府有关系的人都遭受虐待,一切看来没什么不妥。
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So, let's go ahead and think about drawing what that would look like in terms of the radial probability distribution.
让我们来想一想如果把它的,径向概率分布画出来是怎么样的。
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This is the radial probability distribution formula for an s orbital, which is, of course, dealing with something that's spherically symmetrical.
这个ｓ轨道的,径向概率分布公式，它对于球对称,的情形成立。
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So the probability of having an electron at the nucleus in terms of probability per volume is very, very high.
在单位体积内发现,一个电子的概率非常非常大。
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And when we define that as r being equal to zero, essentially we're multiplying the probability density by zero.
当我们定义ｒ等于０处，事实上是把概率密度乘以０．
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For those of you who have had a course in probability and statistics, there will be nothing new here.
对于已经,学过概率和统计的同学来说,这堂课就没什么新鲜的了
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It takes on the value 1 with the probability of 20% and the value of 0 with the probability of 80%.
等于1的概率是20%,等于0的概率是80%
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I've learned that with high probability, the error is not in the first part of the program.
我从这一点得到了什么？,我得到的是错误有很大的可能。
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So, one way we could look at it is by looking at this density dot diagram, where the density of the dots correlates to the probability density.
其中一个理解它的方法,就是通过看这个密度点图，这里点的密度,和概率密度想关联的。
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The highest probability now is going to be along the x-axis, so that means we're going to have a positive wave function every place where x is positive.
概率最高的地方是沿着ｘ轴，这意味着只要在ｘ,大于零的地方波函数都是正的。
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we have Nala and he meets this man, Rituparna, and this is where a probability theory apparently comes in.
有那勒,他遇到的这个人,叫睿都巴若那,这就到了讲概率论的时候了
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You think, some other day, I don't want to talk today about the probability of one of us dying.
你会想,还是改天再说吧,我今天不想讨论家人会有多少可能性会去世
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Right, this makes a lot of sense because if the entire atom was made up of nuclei, then we would have 100% probability of hitting one of these nuclei and having things bounce back.
因为如果整个原子,都是原子核，那我们就有100%概率,撞到一个原子核并被弹回来,所以如果我们。
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So if we actually go ahead and multiply it by the volume of our shell, then we end up just with probability, which is kind of a nicer term to be thinking about here.
乘以壳层的体积,我们就得到了概率，在这里从这个角度，理解问题更好一些,如果我们考虑的是。
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But the reality that we know from our quantum mechanical model, is that we can't know exactly what the radius is, all we can say is what the probability is of the radius being at certain different points.
我们不可能准确的知道,半径是多少，我们只能说，它在不同半径处，的概率是多少，这是,量子力学。
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We're saying the probability of from the nucleus in some very thin shell that we describe by d r.
某一非常薄的壳层dr内,一个原子的概率,你想一个壳层时。
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py And finally, we can look at the 2 p y, so the highest probability is going to be along the y-axis.
最后我们来看一下，概率密度最高的是沿着ｙ轴。
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So if we superimpose our radial probability distribution onto the Bohr radius, we see it's much more complicated than just having a discreet radius.
为波尔半径,这其实比分立的轨道,要复杂很多，我们可以有任何的半径,但有些半径的概率。
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So, you should be able to generally identify and draw the general form of these radial probability distributions.
所以你们应该可以大概辨认,并且画出概率,分布的大致形式。
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Or we could just look at the radial probability distribution itself and see how many nodes there are.
或者我们可以直接,看径向概率分布图,本身看看里面有几个节点。
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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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