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We started talking about these on Wednesday, and what we're going to start with is considering specifically the wave functions for multi-electron atoms.
我们从周三开始讨论这些，而且我们将要以特别地考虑,多电子原子的波函数,为开始。
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And we can also write this in an even simpler form, which is what's called electron configuration, and this is just a shorthand notation for these electron wave functions.
而且我们也可以将它，写为一个更简单的形式，它叫做电子构型,这个仅仅是这些电子波函数的。
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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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Since we're talking about wave functions, since we're talking about the properties of waves, we don't only have constructive interference, we can also imagine a case where we would have destructive interference.
因为我们讨论的是波函数，因为我们讨论的是波的性质，我们不仅有相长干涉，我们也可以想象在,某种情况下会有相消干涉。
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So we can do this essentially for any atom we want, we just have more and more wave functions that we're breaking it up to as we get to more and more electrons.
所以我们基本上对，任何一个原子都可以这么做,我们仅仅会有越来越多的波函数,因为我们将它分为越来越多的电子。
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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 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。
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We can do the exact same thing when we talk about lithium, but now instead of breaking it up into two wave functions, we're breaking it up into three wave functions because we have three electrons.
在讨论锂时,我们也可以做，完全相同的事情,但不是把它分为两个波函数，而是分为三个波函数,因为我们有3个电子。
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If you look in your book there's a whole table of different solutions to the Schrodinger equation for several different wave functions.
如果你们看书的话,上面有一整张,许多，不同波函数,薛定谔方程解的表。
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So instead, these would be canceling out wave functions between the two, so we would end up with a nodal plane down the center.
相反，两者之间的,波函数会相互抵消，所以我们在中间会得到一个节面。
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So, the wave functions for multi-electron atoms.
所以，对于多电子原子的波函数。
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So, as an example, let's take argon, I've written up the electron configuration here, and let's think about what some of the similarities might be between wave functions in argon and wave functions for hydrogen.
所以作为一个例子我们来看看氩，我已经把它的电子构型写在这里，我们来考虑氩和,氢波函数之间的,一些相似性。
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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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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。
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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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So on Friday, we'll start with talking about the wave functions for the multi-electron atoms.
在周五，我们要开始讨论,多电子原子的波函数。
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So now that we can do this, we can compare and think about, we know how to consider wave functions for individual electrons in multi-electron atoms using those Hartree orbitals or the one electron wave approximations.
现在我们可以做这些了，我们可以对比和考虑，我们知道如何用哈特里轨道,或者单电子波近似去考虑,多电子原子中的单个电子波函数,所以对于我们研究了。
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The reason that we can talk about this is remember that we're talking about wave functions, we're talking about waves, so we can have constructive interference in which two different orbitals can constructively interfere, we can also have destructive interference.
我们可以这么说的原因是,记住我们说的是波函数，我们说的是波函数，所以我们可以得到相长干涉,这是两个不同轨道会相长干涉，我们也有相消干涉。
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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 that's somewhat inconvenient because we're working with wave functions, but it's a reality that comes out of quantum mechanics often, which is that we're describing a world that is so much different from the world that we observe on a day-to-day basis, that we're not always going to be able to make those one-to-one analogies.
这对于研究氢原子，很不方便,但这就是事实,而且在量子力学中经常会出现这种事实,那就是我们要描述的世界，和我们日常所看到的世界,之间的差别是如此之大,以至于我们不能，做出一一对应的类比,但幸运的是我们不用管。
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So in this case the cross term represents constructive interference between the two 1 s atomic wave functions.
在这种情况下交叉项代表两个,1s原子波函数的相干干涉。
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And specifically, MO theory is the quantum mechanical description of wave functions within molecules.
特别的，MO理论是,分子内波函数的描述。
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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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So we can draw that for 1 s a, we can also draw it for 1 s b, and what I'm saying for the molecular wave function is that we have the interference between the two, and we have a constructive interference, so we end up adding these two wave functions together.
所以我们可以对1sa画出它来，我们也可以对1sb画出它来，对于分子波函数我要说的是,它们两者之间会干涉，这里我们有相长干涉，所以我们得到的是波两个波函数加起来。
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