-
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。
-
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 have instead what's called a probability density when we have continuous random variables.
所以我们用概率密度的概念来描述,连续型随机变量的情况
-
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, 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。
-
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。
-
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。
-
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。
-
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。
-
This is not a node because a node is where we actually have no probability density.
因为节点处是,没有概率密度的,所以。
-
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。
-
Probability density of finding an electron within that molecule in some given volume.
在分子内某空间找到,一个电子的概率密度。
-
So what is actually going to matter is how closely that electron can penetrate to the nucleus, and what I mean by penetrate to the nucleus is is there probability density a decent amount that's very close to the nucleus.
所以实际上有关系的是,电子可以穿越至原子核有多近,我所指的穿越至原子核是,这里有一定数量的概率密度,可以距离原子核非常近。
-
So, the quantum mechanical interpretation is that we can, in fact, have probability density here and probability density there, without having any probability of having the electron in the space between.
量子力学给出的解释是，实际上，我们可以在这有概率密度，在这里有概率密度,但在两个之间没有。
-
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。
-
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。
-
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。
-
At first it might be counter-intuitive because we know the probability density at the nucleus is the greatest.
起初我们觉得这和直观感觉很不相符,因为我们知道在原子核,出的概率密度是最高的。
-
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。
-
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。
-
So what we should expect to see is one radial node, and that is what we see here 3s in the probability density plot.
个节点,这就是我们，在这概率密度图上所看到的,如果我们考虑。
-
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。
-
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。
-
Think of it as a probability density plot.
把它看成是一个概率密度图。
-
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。
-
PROFESSOR: Probability density, yes.
概率密度。
-
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。
-
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。
-
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。
应用推荐