They're invariably cited as among the most beautiful and exquisite lines in Paradise Lost but on some level they've proven the bane of scholars because they can't be squared with any of the poem's theological message.

它们被单调地引证为,中最美最细致的诗句,但在某些层面他们证明了学者的祸害,因为它们并不能与诗歌所传达的神学信息相一致。

耶鲁公开课 - 弥尔顿课程节选

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。

麻省理工公开课 - 化学原理课程节选

It is telling us that the ground state in lithium would be Z squared.

它告诉我们锂原子的基态,是z的平方。

麻省理工公开课 - 固态化学导论课程节选

The order complexity here, if I actually write it would be-- sorry, order n times m, and if m was equal to n, that would be order n squared, and this is quadratic.

如果m等于n的话,也就是n的平方，这是一个平方复杂度的问题，这是和前面不同类型的，好，我在做什么呢？

麻省理工公开课 - 计算机科学及编程导论课程节选

So this squared at the origin is going to be a very high probability, and it decays off as you get farther and farther away from the nucleus or from the center, and that's independent of the angle.

所以这个平方,在原点处非常高，随着离核子的距离,越来越远,它逐渐衰减，并且它和角度是没有关系的。

麻省理工公开课 - 化学原理课程节选

So what is the wave function squared going to be equal to?

波函数的平方等于什么？

麻省理工公开课 - 化学原理课程节选

And that's going to be equal to negative z effective squared times r h over n squared.

有效的z的平方,乘以RH除以n的平方。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

If you get one over R squared, it'll be a little steeper.

如果你用1除以R的平方，它会变得稍微陡峭一些。

麻省理工公开课 - 固态化学导论课程节选

So because we're feeling a stronger attractive force from the nucleus, we're actually pulling that electron in closer, which means that the probability squared of where the electron is going to be is actually a smaller radius.

因为我们能感到来自原子核,的更强的吸引力，我们实际上会将电子拉的更近，那意味着电子运动的,概率半径是,事实上是一个更小的半径。

麻省理工公开课 - 化学原理课程节选

So, we can do that by using this equation, which is for s orbitals is going to be equal to dr 4 pi r squared times the wave function squared, d r.

用这个方程,对于s轨道，径向概率分布,4πr的平方,乘以波函数的平方,这很容易理解。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

We'll introduce in the next course angular nodes, but today we're just going to be talking about radial nodes, psi and a radial node is a value for r at which psi, and therefore, 0 also the probability psi squared is going to be equal to zero.

将会介绍角节点,但我们今天讲的是，径向节点，径向节点就是指，对于某个r的值,当然，也包括psi的平方，等于,当我们说到s轨道时。

麻省理工公开课 - 化学原理课程节选

We call that a node, r and a node, more specifically, is any value of either r, the radius, or the two angles for 0 which the wave function, and that also means the wave function 0 squared or the probability density, is going to be equal to zero.

节点就是指对，于任何半径，或者，两个角度,波函数等于，这也意味着波函数的平方或者概率密度,等于，我们可以看到在1s轨道里。

麻省理工公开课 - 化学原理课程节选