In this state, each atom's quantum wave-function-its effective size-extends several billionths of a metre from its nucleus.
在这种状态下，每一个原子的量子微波函数- - -即它的有效作尺寸- - -将以原子核为中心延展到十亿分之几米(即纳米)的范围。
But we do have an interpretation for wave function squared.
但波函数的平方我们有一个解释。
If it is small enough, then its wave function will also spread out over a space large enough for it to penetrate more than one slit simultaneously.
如果它足够小，那么它的波函数也会穿越对它足够大的空间而传播，在同一时刻穿过一个以上的缝隙。
But before we get to that, in terms of thinking just think, OK, this is representing my particle, this is representing my electron that's what the wave function is.
但是在我们谈论那个部分之前，在理解方面，仅仅是理解，好的，它代表了粒子，它代表了电子，这就是波函数。
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。
So if we're talking about probability density that's the wave function squared.
如果我们要讨论概率密度，这是波函数的平方。
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。
But now we're talking not about an atomic wave function, we're talking about a molecular wave function.
但现在我们不是讨论原子的波函数，我们讨论的是分子的波函数。
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。
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。
So again, we can think about the probability density in terms of squaring the wave function.
同样的，我们可以把，波函数平方考虑概率密度。
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。
So, we have now a complete description of a wave function that we can talk about.
所以我们现在得到了，波函数，的完整描述。
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？
There's no classical way to think about what a wave function is.
我们没有办法从经典力学的角度,想象波函数是什么样的，没有经典的类比。
So, we can think about what is it that we would call the ground state wave function.
我们来考虑一下，基态的波函数，是怎么样的。
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。
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。
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。
So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
这就是概率密度，但作为，把它当成是，波函数的解，让我们先倒回来一点。
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。
No matter where you specify your electron is in terms of those two angles, it doesn't matter the angular part of your wave function is going to be the same.
不论你将，这两个角度，取成什么值，波函数的角向部分，都是，相同的。
So what is the wave function squared going to be equal to?
波函数的平方等于什么？
So, the wave function at all of these points in this plane is equal to zero, so therefore, also the wave function squared is going to be equal to zero.
因此这里的,波函数平方也等于零，如果我们说在这整个平面上,任何地方找到一个p电子的概率都是零。
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。
It makes sense to draw the wave function as a circle, because we do know that 1 s orbitals are spherically symmetric.
把波函数画成一个圆是有道理的，因为我们知道1s轨道是球对称的。
But in sigma orbitals, you have no nodal planes along the bond axis, so if we had a nodal plane here, we'd see an area where the wave function was equal to zero.
但在sigma轨道里，沿着轴向是没有节点平面的，如果我们有个节点，我们就会看到某个地方波函数等于0。
So, we can say that a circle is a good approximation for a 1 s wave function.
所以我们说一个圆是，对1s波函数的好的近似。
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？
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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