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So when you operate on the wave function, what you end up with is getting the binding energy of the electron, and the wave function back out.
所以当你将它作用于波函数时，你得到的是电子的结合能,和后面的波函数。
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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。
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So, in all of this, what he does is he makes, to use an expression that I've already used before in the context of absolutism, he makes the Boyars, while he's building his navy and expanding Russia, he makes the Boyar junior partners in absolutism.
所以,通过所有的这些事情,用我之前用过的一个词来形容,他使得波维尔们,当他在建海军和扩张领土时,他使得波维尔贵族臣服在他的绝对权威之下
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We also talked about well, what is that when we say wave function, what does that actually mean?
我们还说了，当我们讨论波函数时，它到底有什么意义？
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And when we're talking about the amplitude of the wave, we're talking about the deviation from that average level. So, if we define the average level as zero, you can have either a positive amplitude or a negative amplitude.
当我们讨论一个波的振幅时,我们说的是偏离平均位置的量,如果我们把平均位置,定义为零的话，那幅值不是,正的就是负的，有时候人们在。
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So, remember this makes sense if you just think of it as a wave and forget the particle part of it for right now, because that would be very upsetting to think about and that's not, in fact, what's going on, we're talking about quantum mechanics here.
记住如果你们把它看做是一个波,而忘记它是一个粒子时，这就是可以理解的了，因为如果把它看做,一个粒子就行不通了，实际上也不是这样的，这里我们是以量子力学的角度来考虑问题。
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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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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。
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while we do, in fact, have the wave function plots up here.
这里已经画了波函数，但看这些图时一个关键的地方。
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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。
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l But now we need to talk about l and m as well. So now when we talk about a ground state in terms of wave function, we need to talk about the wave function of 1, 0, 0, and again, as a function of r, theta and phi.
但我们现在需要讨论,和m，现在当我们讨论,波函数的基态时，我们讨论的，是1，0，0的波函数，同样的，它也是r，theta和phi的函数。
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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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pxa So what happens when we add a 2 p a and we subtract from it a 2 p x b, or the same with a 2 p y a subtracting a 2 p y b, is that we're actually going to cancel out the wave function in the center, so we now have 2 nodal planes.
当我们用,减去2pxb时，或者是2pya减去2pyb时，我们会消去,中间的波函数，所以现在我们有两个节面。
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Oh, and actually before you skip your page in the notes, I realized I should write out for you what the addition is to start with. So, when we're combining two waves, 1sb what we have is 1 s a that we're adding together with 1 s for b, the second atom.
在你们翻过这页讲义之前，我觉得我应该写出加法,当我们把两个波函数放在一起时，我们用1sa加上，第二个原子。
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