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The Colts defeated the Chicago Bears for the N.F.L.championship.
VOA: special.2010.02.05
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And we talked about the equation you can use for radial nodes last time, and that's just n minus 1 minus l.
我们讲过这个用于,计算径向节点的方程，也就是ｎ减去ｌ减去１
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PROFESSOR: OK. We can have n 4, l 3, and then, sure, we can have m sub l equal negative 2 if l equals 3 What's the second value of l that we can have?
教授：嗯，我们有ｎ４，ｌ３,然后我们有ｍｌ等于－２，如果ｌ等于３,ｌ可以有的第二个值是多少？
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"That's kind of fun!" "What's your name?" "Broklin,B-R-O-K-L-I-N."
VOA: special.2010.04.30
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It turns out there's a new function strlen S-T-R-L-E-N that you probably have not used yet called strlen, S-T-R-L-E-N, programmers early on and still like to be succinct but communicates sufficiently what they mean.
结果这里有个新的函数,你可能没有使用过，叫做，早期的和现在的程序员喜欢简洁地,但是能充分的传达他们的意思。
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The address is u-s-a-l-e-a-r-n-s dot o-r-g.
VOA: special.2009.01.15
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Why didn't they keep right on going with G, H, I, J, K, L, M, N, O, P?
为什么他们不接着写下去呢,按照字母表
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n l m s Once we have chosen a certain mix of n, l, m and s, it is used once for that particular atom.
一旦我们选定了一组量子数，它就只能被一个固定原子所有。
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The other main difference that we're really going to get to today is that in multi-electron atoms, orbital energies depend not just on the shell, which is what we saw before, not just on the value of n, but also on the angular momentum quantum l number. So they also depend on the sub-shell or l.
我们今天要讨论的,另一个很重要的区别就是,在多电子原子中，轨道能力不仅仅依赖于，我们以前看到的外层，不仅仅依赖于n的值，而是与角动量量子数也有关系,所以它们也依赖于亚外层或者。
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And we can calculate that with the formula that we used, which was just n minus l minus 1 equals the number of nodes.
这个我们可以用我们以前用过的那个公式来计算，也就是节点数等于ｎ减去ｌ减去１
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STUDENT: PROFESSOR: Oh, I'm sorry. So it's n minus l minus 1.
学生：,教授：不好意思，这是ｎ减去ｌ减去１．
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If we have n equals 4, what is the highest value of l that we can have?
如果ｎ等于４,ｌ的最大值是多少？
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n*pi/L It turns out it is n pi over l.
结果是。
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In contrast, if we're taking the wave function and describing it in terms of n, l, m sub l, and now also, the spin, what are we describing here?
相反，如果我们考虑一个波函数,然后用ｎ，ｌ，ｍ小标ｌ,还有自旋，我们描述的是什么？
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And is no longer that sole determining factor for energy, energy also depends both l on n and on l.
对于能量的,唯一决定性因素,它也依赖于n和。
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And the complete description, as I said, n l m is from n l and m.
我说过完整的描述，需要。
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So let's just think exactly what this means, and that means that if we take away function and we define it in terms of n, l and m sub l, what we're defining here is the complete description of an orbital.
让我们来考虑一下这是什么意思，这是说如果我们不考虑波函数,而是用ｎ，ｌ，ｍ下标ｌ来定义它，我们定义的,是一个轨道的完整描述。
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And unlike n, l can start all the way down at 0, and it increases by integer value, so we go 1, 2, 3, and all the way up.
不像n，l可以从0开始取，然后每次增加一个整数，所以我们可以去1，2，3，一直下去。
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Just by n, l, m, s is inadequate.
仅仅靠n，l，m，s是不够的。
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We'll get to discussing that, but what I want to point out here again is the fact that instead of just being dependent on n, the energy level is dependent on both n and l.
我们将要讨论它，但是我想指出的是事实上能级不只是与n有关,而是与n和l都有关系，而且n不再是。
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s We are back over to E as a function of n, l, m and s, only we got there through this other torturous route.
我们回到将E作为函数n，l和，只要我们解决了这个烦人的路径。
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So if we have a 3 d orbital, we're talking about n minus l minus 1, what is n equal to? What is l equal to?
如果我们有一个3d轨道，我们用ｎ减去ｌ减去１,ｎ等于多少？ｌ等于多少？
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n l So negative e, which is sub n l, because it's a function of n and l in terms of quantum numbers.
也就是负的，E，下标是，因为它是一个,关于量子数，n，和，l，的函数。
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So, it would be a good question to ask n why are we limited clearly there's this relationship between l and n, and we can't get any higher than n equals one.
那我们要问了,为什么我们被限制了，很明显，l和,有关系，为什么不能取到，n-1更大的值。
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Again, the reason for that is because the energy only depends on the n value here, it doesn't depend on l or on m.
因为，能量,只和n的值有关，与l和m的值无关。
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So, our next level up that we can go is going to be the n equals 2 energy level, but we also have an l and an m value, 0 so our lowest l is going to be a there.
所以下一个能量,是n等于2的能级，但我们还有l和m的值，所以我们最低的l等于。
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So if we say that l is just talking about our kinetic energy part, our rotational kinetic energy, and we know that electrons have potential energy, then it makes sense that l, in fact, can never go higher than n.
如果我们说，l仅仅是,描述动能项，我们的旋转动能，我们知道，电子有势能，所以可以理解，l不能比n高。
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So finally, if we talk about our last example of when n is going to be equal 2, l -1 and then minus 1 for m.
最后我们要讲的,这个例子，是n等于2时，等于1，we，can，have，2，，1，for，l,而m等于。
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ml=-2 So let's say we have n equals 4, and n sub l equalling negative 2.
这里n等于。
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But also unlike n, l cannot have just any value, we can't go into infinity.
但不像n，l，不能取所有整数，不能到正无穷。
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