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And today we'll finish that discussion, and, of course, point out actually the failure of classical mechanics to appropriately describe what's going on in an atom.
结束这部分的讨论，当然的，要指出经典力学,在描述原子内部,情况时是失败的。
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And in this case we're going to look at silicone, and we'll say if you can point out to me which requires the least amount of energy.
这次我们要做的是关于硅的，我们来看看大家是不是,能够为我指出那一项需要消耗的能量最少。
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But before I get started, I have to point out something a little bit unusual about this class We're being filmed.
但在我开始之前,我要告诉大家这个课程的一点特别之处,我们会被录像
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I'll point out that in-house language throughout the semester, and we'll talk about how it should be interpreted.
我会在课上指出哪些是黑话，我们会讨论应该如何翻译。
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And I'll point out as we proceed, because I kind of have to start using the cloud here.
稍后我会继续指出，我们需要,开始使用云了。
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I've begun to point out a few things that I think we miss: the fragmentation of bodies.
这就是我要指出的,我觉得大家错过了的东西。
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The reason I want to point this out to you is, if we go back up to the kinds of data objects we started with, floats, ints, strings, they actually behave the same way.
我要为大家指出这一点的原因是，如果我们想一下以前讲过的,数据类型的种类，浮点数，整数，字符串，它们实际上有相同的行为方式。
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And of course, the hedonist will also hasten to point out that just because we can't do this perfectly or infallibly, that doesn't mean we can't make educated guesses, right?
当然享乐主义者也会急于指出,不能因为无法完美绝对地做到，就意味着不能做出有根据的猜想？
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Now, we could walk out the door at that point, right?
在这里,我们就已经觉得差不多了
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Another reason I wanted to point this out in terms of the polar coordinates that we're using, is I think they're actually flipped from what you're used to seeing in physics.
另一个我想指出,我们采用极坐标的原因是，我认为它们实际上是,从你们习惯于看到的物理学中出来的。
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So, first, if I point out when l equals 0, when we have an s orbital, what you see is that angular part of the wave function is equal to a constant.
首先，如果ｌ等于０,那就是ｓ轨道，你们可以看到,它波函数的角度部分是一个常数。
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Another thing to point out in these two graphs is that we do have nodes, and we figured out last time, we calculated how many nodes we should have in a 2 s orbital.
另外这两张图上要指出的是,我们可以看到节点，上次我们知道，我们算了２ｓ轨道有多少个节点。
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So even though we see a nodal plane down the center, I just want to really point out that it's only when we have a nodal plane in the internuclear or the bond axis that we're calling that a pi orbital.
虽然在中间有个节面，我想要指出的是,只有节面在核间轴,或者键轴上时,我们才叫它π轨道。
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But just to point out the confusion can be we've actually switched what the question is here.
他们有这些幻灯片的拷贝,这里要指出容易混淆的地方是。
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I want to point out that the zero energy is defined as when you have a naked proton -- where the electron has popped out -- that's what we've defined as zero energy up to this point when we're talking about single atoms.
我想指出，这里零点能的定义,是当我们只有一个裸露的质子,而没有电子时-,到目前为止对零点能一直采用这样的定义,当我们在讨论单个原子时。
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And again, I want to point out that a molecular orbital, we can also call that a wave function, they're the same thing.
同样，我要指出的是,一个分子轨道，我们也可以叫它波函数，这是一件事情。
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So what I want to point out is 3d2 what we said now is that the 3 d 2 is actually lower in energy, so if we were to rewrite this in terms of what the actual energy order is, 3d2 4s2 we should instead write it 3 d 2, 4 s 2.
所以我们想指出的是,我们现在所说的是,实际上能量比较低，所以如果我们重新的,写出实际的能量顺序，我们应该写出。
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So, this is actually kind of neat to point out, because we all remember J.J. Thomson Thomson J J Thomson from our second lecture, and J.J. Thomson got a Nobel Prize in 1906 for showing that electrons exist in that they are particles.
所以，这个确实需要要指出，因为我们都记得第二堂课,讲到的,因为发现了电子具有粒子性,在1906年获得了诺贝尔奖。
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So that's why we have this zero point here, and just to point out again and again and again, it's not a radial node, it's just a point where we're starting our graph, because we're multiplying it by r equals zero.
这就是为什么在这里有个零点，我需要再三强调，这不是径向零点，他只是我们画图的起始处，因为我们用ｒ等于０乘以它。
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What I want to point out also is that this h hat, the Hamiltonian operator written out for the simplest case we can even imagine, which is a hydrogen atom where we only have one electron that we're dealing with, and of course, one nucleus.
我也想指出的是，我们能想到的最简单情况,的哈密顿算符，是一个只有一个电子,也只有一个原子核的氢原子。
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And the thing I wanted point out is, we've got this global variable number of calls. Which is there not because Fibonacci needs it but just for pedagogical reasons, so that we can keep track of how much work this thing is doing.
要指出的是我们已经,调用了几次这个全局变量,这不是因为斐波那契数列,需要调用它而只是,因为教学上的需要，以便我们可以知道,这个函数做了多少事情。
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I was going to start showing you some examples, but I think, rather than doing that, I'm going to stop here, I'm going to give you two minutes back of time, but I want to just point out to you that we are going to have fun next week, because I'm going to show you what in the world that has to do with efficiency.
我想再给你们讲解一些例子，但是我想想还是算了吧，给你们两分钟休息时间,但是我想告诉你们,我们下周的课,会很有意思,我会告诉你们,到底是什么决定了效率。
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And what I want to point out that we just figured out for molecular orbital theory, is that o 2 is a biradical, because remember, the definition of a radical is when we have an unpaired electron.
我要指出的是,我们刚利用分子轨道理论，指导了O2是二价自由基，因为记住，自由基的定义是,有个未配对的电子。
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Another thing I want to point out about every sigma orbital that you see, and it will make more sense when we contrast it with pi orbitals later.
另外一个我要指出的事情就是,关于每个sigma轨道你能看到,当我们把它和π轨道对比的时候会看的更清楚。
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And when we make these comparisons, one thing I want to point out is that we need to keep the constant principle quantum number constant, so we're talking about a certain state, so we could talk about the n equals 2 state, or the n equals 3 state.
当我们做这些比较时，我想指出的一件事是,我们需要保持常量原则,保持量子数是常数，所以我们在讨论一个确定的态时，我们可以谈论n等于2的态，或者n等于3的态。
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And here's a little trick -- and again, we promised to point -- out little tricks of the trade -- if I know I want to execute the last command I typed that started with an m, bangm will actually figure out what that command was and redo it for me so I don't have to figure it out, or you can go back in time in a terminal window.
这里有个小技巧--此外，我们许诺指出行业中的,一些小技巧-,如果我知道我想执行我写入的上一个命令,是以m开头的，！m会明白那个命令是什么,然后为我恢复上次操作,所以我不需要明白它，或者你可以回到,那个终端窗口。
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So really what I want to point out here is as we get more into describing quantum mechanics these quantum dots are one really good example where a lot of the properties of quantum mechanics apply directly. So, if you're interested, I put the Bawendi lab research website onto your notes.
我真正想说的是，随着,我们学习量子力学的深入,这些量子点是很多量子,力学性质得到直接应用的很好例子,如果你们感兴趣的话，我把Bawendi实验室的,网站放到你们的讲义里去。
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We've got some chords set out and we're going to-- we've got some chords set out here and we're in the key of C at this point, and we're going to hear Beethoven go to a tonic chord, then a sub-dominant chord, then a tonic chord, then a dominant chord and so on.
我们看到有一些和弦-,而我们现在在C调的位置上，然后听贝多芬的主音和弦，然后是次属音和弦，然后是主音和弦，接着是属音和弦，如此往复。
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