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。

麻省理工公开课 - 化学原理课程节选

So I'm going to wave my hands at what one fflush of these things here does, fflush here, but I decided this is kind of a weak implementation.

所以我将向这些东西所做的挥手,这里的，但是我觉得这是个有点无力的实现。

哈佛公开课 - 计算机科学课程节选

So, for example, if we were looking at the actual wave function, we would say that these parts here have a positive amplitude, and in here we have a negative amplitude.

我们看，一个波函数,我们说，它这部分幅值，为正,这部分幅值为负，当我们看。

麻省理工公开课 - 化学原理课程节选

It seems to depict a storm at sea, almost as if the Egyptians are in boats, and a big wind makes a giant wave, and another wind then makes it crash down on them.

而是描述了一阵风，就像埃及士兵在船上,狂风掀起大浪，另一阵风，掀翻了船。

耶鲁公开课 - 旧约导论课程节选

I want to get there by wave mechanics to arrive at the same place.

我想通过波动力学到达,与此相同的地方。

麻省理工公开课 - 固态化学导论课程节选

The first wave was in the 1960s and, at that time, Congress had limits-- state governments had limits on the interest that savings banks could pay people on their accounts.

在20世纪60年代,那时候国会限制了...,各州政府给储蓄银行,设定了账户利率的支付上限

耶鲁公开课 - 金融市场课程节选

Wave. Wave to mom at home.

挥手,跟屏幕前的老妈打个招呼

耶鲁公开课 - 博弈论课程节选

All right. So let's look at some of these wave functions and make sure that we know how to name all of them in terms of orbitals and not just in terms of their numbers.

好，让我们来看一下,这些波函数,并确定我们都知道,怎么用轨道,而不仅是量子数来命名它们,一旦我们可以命名它们。

麻省理工公开课 - 化学原理课程节选

We looked at the wave functions, we know the other part of solving the Schrodinger equation is to solve for the binding energy of electrons to the nucleus, so let's take a look at those.

我们看过波函数，我们知道解,薛定谔方程的其他部分,就是解对于原子核的电子结合能，所以我们来看一看。

麻省理工公开课 - 化学原理课程节选

Again we can look at this in terms of thinking about a picture this way, in terms of drawing the wave function out on an axis.

同样我们可以,用这个图像来考虑，从画轴上的波函数来考虑。

麻省理工公开课 - 化学原理课程节选

And you can think about that if you think about a standing wave, for example, where you can have amplitude at many different values of x, so an amplitude at many different distances, but you also have areas where there is a amplitude.

你们可以想象一下驻波，在不同ｘ处,可以有不同的振幅，在不同的距离有不同的振幅，但在某些地方振幅等于０．

麻省理工公开课 - 化学原理课程节选

So, at this place where it hits zero, 0 that means that the square of the wave function is also going to be zero, right.

它达到0的地方，这意味着波函数的，平方也是,如果我们看概率密度图。

麻省理工公开课 - 化学原理课程节选

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

So, you remember from last time radial nodes are values of r at which the wave function and wave function squared are zero, so the difference is now we're just talking about the angular part of the wave function.

你们记得上次说径向节点在,波函数和波函数的平方,等于零的ｒ的处，现在的区别是我们讨论的是,角向波函数。

麻省理工公开课 - 化学原理课程节选

So, if we look at the bottom here and the actual plot of the wave function, we see it starts high, very positive, 0 and it goes down 0 and it eventually hits zero, and goes through zero 0 and then becomes negative 0 and then never quite hits zero again, although it approaches zero.

我们看,这下面这是波函数，我们看到它开始很高，是正的，然后降低直到,然后它穿过，变成负的,最后接近,但没达到，在这个。

麻省理工公开课 - 化学原理课程节选

So, what this means is that when we're looking at an actual wave function, we're treating it as a wave, right, so waves can have both magnitude, but they can also have a direction, so they can be either positive or negative.

这意味着,当我们看一个波函数时,我们把它看做一个波，波不仅有幅值，还有方向，所以它们可正可负，如果。

麻省理工公开课 - 化学原理课程节选

So, we can look at other radial probability distributions of other wave functions that we talked about.

我们可以来看一看我们讨论过的,其它一些波函数的径向概率分布。

麻省理工公开课 - 化学原理课程节选

So, most people could recognize that light wave a has the shorter wavelength. We can see that just by looking at the graph itself -- we can see certainly, this is shorter from maxima to maxima.

0秒钟，好的，不错大部分,同学都可以判断出来这个光波的,波长更短，我们仅通过,看图就能看出来-可以。

麻省理工公开课 - 化学原理课程节选

So again, if we think of a graph of the wave function, we had the wave function is at its highest amplitude when it's lined up with the nucleus, and then as we got further away from the nucleus, the amplitude of the wave function ends up tapering off until it never hits zero exactly, but it goes down very low.

同样，如果我们想象一幅波函数的图，波函数在原子核的位置上,有着最高的振幅，随着与原子核距离变远，波函数振幅逐渐变小直到,它永远不会到零，但它会变得很小。

麻省理工公开课 - 化学原理课程节选

So when we talk about a wave function squared, n l m he wave function, any one that we specify between n, l and m, at any position that we specify based on r, theta, and phi.

一个波函数,的平方时，对特定,特定位置r，theta，phi波函数，取平方,如果我们取平方。

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

More interesting is to look at the 2 s wave function.

看2s轨道波函数,更加有趣。

麻省理工公开课 - 化学原理课程节选

In contrast when we're looking at a p orbital, so any time l is equal to 1, and you look at angular part of the wave function here, what you see is the wave function either depends on theta or is dependent on both theta and phi.

相反当我们看ｐ轨道时，任何时候ｌ等于１,你们看它的角向波函数，你们可以看到它要么是和theta有关,要么是和theta和phi都有关。

麻省理工公开课 - 化学原理课程节选

The more important thing that I want you to notice when you're looking at this wave equation for a 1 s h atom, is the fact that if you look at the angular component of the wave function, you'll notice that it's a constant.

我要你们注意的,更重要的一点是,当你们看到,这个氢原子1s轨道方程的时候，如果你们看,波函数，的角向部分，你们会发现它是一个常数。

麻省理工公开课 - 化学原理课程节选