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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.
我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。
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You get these plots by taking the wave function times its complex conjugate and operating on that.
你也可以得到这些，通过波函数乘以,其共轭进行如上操作。
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There's no classical analogy that explains oh, this is what you can kind of picture when you picture a wave function.
可以解释：,哦，这就是，你想象的,波函数的样子啊。
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So we saw that our lowest, 1 0 0 our ground state wave function is 1, 0, 0.
我们看到最低的，或者基态波函数是。
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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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But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.
波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。
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And the person we have to thank for actually giving us this more concrete way to think about what a wave function squared is is Max Born here.
需要感谢，马克思，波恩,给了我们，这个波函数平方的,具体解释，事实上。
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The highest probability now is going to be along the x-axis, so that means we're going to have a positive wave function every place where x is positive.
概率最高的地方是沿着ｘ轴，这意味着只要在ｘ,大于零的地方波函数都是正的。
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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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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, for example, if we were looking at the actual wave function, we would say that these parts here have a positive amplitude, and in here we have a negative amplitude.
我们看，一个波函数,我们说，它这部分幅值，为正,这部分幅值为负，当我们看。
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Remember this is our bond axis here, and you can see there is this area where the wave function is equal to zero all along that plane, that's a nodal plane.
记住这是我们的键轴，你可以看到在这些区域,波函数在这个面内全都是零，这是节点面。
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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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We can't actually go ahead and derive this equation of the wave function squared, because no one ever derived it, it's just an interpretation, but it's an interpretation that works essentially perfectly.
从这个方程中,导出，波函数的平方，没有人可以这样做，这仅仅是一种解释，但这种解释，能解释的很好，自从它第一次被提出来之后。
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Ever since this was first proposed, there has never been any observations that do not coincide with the idea, that did not match the fact that the probability density is equal to the wave function squared.
从未有，任何观测，与它相抵触,从没有过，波函数的平方不等于,概率密度的情况，关于马克思，波恩。
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And first we discussed the fact that well, in terms of a classical analogy, we don't really have one for wave function, we can't really think of a way to picture wave function thinking in classical terms.
首先我们说了，波函数没有一个，经典的类比，我们不能想象一个,经典的波函数的图像。
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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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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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But right now, what I want you to be thinking of a wave function as is just some representation of an electron.
但是现在，我想让你们,将波函数仅仅理解为,一个电子的表示方法。
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And on Monday what we were discussing was the solution to the Schrodinger equation for the wave function.
周一我们讨论了,薛定谔方程解的波函数。
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It's going to be positive in terms of its wave function or in terms of its phase anywhere where y is positive.
只要ｙ大于零它的波函数,或者说是相位为正。
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psi I mentioned that we can also solve for psi here, which is the wave function, and we're running a little short on time,
我说过我们也可以解,波函数，我们讲的稍微有点慢，
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so, remember we can break up the total wave function into the radial part and the angular part.
记住我们可以把整体波函数,分解成径向部分和角向部分。
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We're seeing that the wave function's adding together and giving us more wave function in the center here.
我们看到波函数加在一起,使中间的波函数更多了。
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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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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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psi1 0 0 We can call that psi 1, 0, 0, is how we write it as a wave function.
我们可以叫它，这是我们作为波函数的形式写出它。
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So again if we look at this in terms of its physical interpretation or probability density, what we need to do is square the wave function.
如果我们从物理意义或者,概率密度的角度来看这个问题，我们需要把波函数平方。
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Again we can look at this in terms of thinking about a picture this way, in terms of drawing the wave function out on an axis.
同样我们可以,用这个图像来考虑，从画轴上的波函数来考虑。
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