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It looks like just about everyone is able to go from the name of an orbital to the state function.
看来基本上大家都能从一个,给出的轨道名字得到它的波函数了。
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So we can go on and do this for any orbital or any state function that we would like to.
我们可以继续，对任何轨道,或任何波函数做，同样的事情。
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What we are going to say is that the wavefunction for molecular orbitals is going to be an additive sum of the wavefunctions of atomic orbitals.
我想说的是,分子轨道的波函数,就是多个原子轨道,波函数的线性叠加。
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If we overlay what the actual molecular orbital is on top of it, what you see is that in the center you end up cancelling out the wave function entirely.
如果我们把真实的分子轨道覆盖在上面，你可以看到中间的,波函数是完全抵消掉了。
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So, we're talking about wave functions and we know that means orbitals, but this is -- probably the better way to think about is the physical interpretation of the wave function.
我们讨论波函数而且,我们知道它代表着轨道，但-也许更好的思考方法是,考虑波函数的物理意义。
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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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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。
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We talked about the wave function for a 2 s orbital, and also for a 3 s orbital.
我们讲过２ｓ轨道的波函数，也讲过３ｓ轨道。
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So we do, in fact, have a dependence on what the angle is of the electron as we define it in the orbital.
实际上当我们定义电子在这个轨道,它的波函数的确是和角度有关的。
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This is a table that's directly from your book, and what it's just showing is the wave function for a bunch of different orbitals.
这是一张你们书里的表格，它展示了各种,不同的轨道波函数。
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So, saying wave functions within molecules might sound a little confusing, but remember we spent a lot of time talking about wave functions within atoms, and we know how to describe that, we know that a wave function just means an atomic orbital.
说分子内的波函数可能,听着有点容易搞混，但记住我们花了很多时间,讨论了原子中的波函数，而且我们知道如何去描述它，我们知道波函数意味着原子轨道。
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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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And in doing that, we'll also talk about the shapes of h atom wave functions, specifically the shapes of orbitals, and then radial probability distribution, which will make sense when we get to it.
为了这样做，我们要讲一讲，氢原子，波函数的形状，特别是轨道的形状，然后要讲到径向概率分布，当我们讲到它时，你们更能理解。
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It's the same thing with molecules a molecular wave function just means a molecular orbital.
这对于分子也是一样,分子波函数就意味着分子轨道。
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So the probability again, that's just the orbital squared, the wave function squared.
同样，概率密度，这就是轨道的平方，波函数的平方。
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And in either case if we first talk about constructive interference, what again we're going to see is that where these two orbitals come together, we're going to see increased wave function in that area, so we saw constructive interference.
在任何情况下,如果我们首先讨论相长干涉的话，我们同样会看到,当这两个轨道靠拢的时候，我们看到这个区域有波函数增加，所以我们看到的是相长干涉。
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And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.
此外，当我们解波函数,或者考虑薛定谔方程的结果时，我们看到的确３个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。
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When we're talking about orbitals, we're talking about wave functions.
当我们说轨道的时候，我们说的是波函数。
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And what we end up forming is a molecular orbital, because as we bring these two atomic orbitals close together, the part between them, that wave function, constructively interferes such that in our molecular orbital, we actually have a lot of wave function in between the two nuclei.
最后我们得到了分子轨道，因为当我们把这两个原子轨道放在一起的时候，它们之间的部分，波函数，相干相加，所以在分子轨道里，我们在两个原子核之间有很多波函数。
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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。
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And the significant difference between s orbitals and p orbitals that comes from the fact that we do have angular momentum here in these p orbitals, is that p orbital wave functions do, in fact, have theta and phi dependence.
轨道和ｐ轨道的,不同之处在于,在ｐ轨道，波函数，随theta和phi变化。
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More interesting is to look at the 2 s wave function.
看2s轨道波函数,更加有趣。
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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。
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So they're the same shape, this is the shape of the orbital or the shape of the wave function, and we can call this either 2 p x a being combined with 2 p x b, or we could say since it's the same shape, it's 2 p y a being combined with 2 p y b.
它们形状是一样的，这是轨道的形状或者波函数的形状，我们叫它2pxa和2pxb结合，或者我们说因为它们的形状是一样的，它是2pya和2pyb结合。
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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。
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