-
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。
-
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。
-
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。
-
These are called population measures because they refer to the whole population of possible outcomes and they measure the probabilities.
这些是用来度量总体的变量,因为他们对应的是总体中所有的结果,度量的是所有事件的概率
-
In the investment game, the more likely I was to invest, the more likely you, the more you wanted to invest.
在投资博弈中我投资的概率越大,你们也就越想要投资
-
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。
-
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。
-
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．
-
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。
-
It's about how so many plans in finance are messed up by rare events that suddenly appear out of nowhere.
书中提到金融界中突然出现的小概率事件,怎样搞砸了无数计划
-
The more you thought other people were going to invest, the more likely that you were going to invest.
你越觉得大家都会投资,你投资的概率就越大
-
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。
-
We will always have r equals zero in these radial probability distribution graphs, and we can think about why that is.
在这些径向概率分布图里,总有ｒ等于０处，我们可以考虑为什么会这样。
-
So, doing those probability density dot graphs, we can get an idea of the shape of those orbitals, we know that they're spherically symmetrical.
概率密度点图上,我们可以对这些轨道的形状，有个大概了解,我们知道它们是球，对称的,我们今天不讲。
-
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。
-
And when we do that we can see this curve, this probability curve, where we have a maximum probability of finding the electron this far away from the nucleus.
当我们这样做时，我们可以看到这个曲线，这个概率分布曲线，这里有发现,电子的最大概率。
-
So we can see if we look at the probability density plot, we can see there's a place where the probability density of is actually going to be zero.
就能看到,有些地方，找到一个电子的,概率密度,我们可以考虑。
-
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。
-
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
-
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%
-
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
-
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。
-
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。
-
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
-
We can not do that with quantum mechanics, the more true picture is the best we can get to is talk about what the probability is of finding the electron at any given nucleus.
在量子力学里我们不这样做，我们能得到的更加真实的图像,是关于在某处,找到电子的概率。
-
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。
-
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。
-
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。
-
And the reason that they're the least sheilded is because they can get closest to the nucleus, so we can think of them as not getting blocked by a bunch of other electron, because there's some probability that they can actually work their way all the way in to the nucleus.
它们最不容易被屏蔽的原因,是因为他们可以更加接近原子，所以我们可以认为它们,最不容易被其它原子阻挡住，因为它们有一定的概率,离原子核非常近。
-
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。
应用推荐