这些波函数就是特征函数。
当我们说轨道的时候，我们说的是波函数。
When we're talking about orbitals, we're talking about wave functions.
周一我们讨论了，薛定谔方程解的波函数。
And on Monday what we were discussing was the solution to the Schrodinger equation for the wave function.
如果我们要讨论概率密度，这是波函数的平方。
So if we're talking about probability density that's the wave function squared.
我们讲过2s轨道的波函数，也讲过3s轨道。
We talked about the wave function for a 2 s orbital, and also for a 3 s orbital.
同样的，我们可以把，波函数平方考虑概率密度。
So again, we can think about the probability density in terms of squaring the wave function.
所以我们说一个圆是，对1s波函数的好的近似。
So, we can say that a circle is a good approximation for a 1 s wave function.
我说过我们也可以解,波函数，我们讲的稍微有点慢
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
同样，概率密度，这就是轨道的平方，波函数的平方。
So the probability again, that's just the orbital squared, the wave function squared.
这对于分子也是一样，分子波函数就意味着分子轨道。
It's the same thing with molecules a molecular wave function just means a molecular orbital.
我们也可以看看，2,1,0态波函数，它是。
Then we can also talk about the 2, 1, 0 state function, psi2 1 0 which would be psi 2, 1, 0.
记住我们可以把整体波函数，分解成径向部分和角向部分。
So, remember we can break up the total wave function into the radial part and the angular part.
在这种情况下交叉项代表两个，1s原子波函数的相干干涉。
So in this case the cross term represents constructive interference between the two 1 s atomic wave functions.
我们看到波函数加在一起，使中间的波函数更多了。
We're seeing that the wave function's adding together and giving us more wave function in the center here.
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。
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.
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。
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.
我们还说了，当我们讨论波函数时，它到底有什么意义？
We also talked about well, what is that when we say wave function, what does that actually mean?
在氢原子A里，我在这里把原子核画成一个点，这圆就是波函数。
So in hydrogen atom a, I'll depict that here where the nucleus is this dot, and then the circle is what I'm depicting as the wave function.
要讨论它的波函数，我们说它是sigma1s的平方。
So to talk about it's squared, we're going to say it's sigma 1 s squared.
我们可以继续，对任何轨道,或任何波函数做，同样的事情。
So we can go on and do this for any orbital or any state function that we would like to.
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。
It makes sense to draw the wave function as a circle, because we do know that 1 s orbitals are spherically symmetric.
这个方程的解法是，看起来像是写成数学符号就是，波函数。
And the solution to this equation looks like this where it is written in terms of a quantity called a wavefunction.
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。
So instead, these would be canceling out wave functions between the two, so we would end up with a nodal plane down the center.
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。
It looks like just about everyone is able to go from the name of an orbital to the state function.
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。
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.
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。
But now we're talking not about an atomic wave function, we're talking about a molecular wave function.
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。
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.
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。
And again, I want to point out that a molecular orbital, we can also call that a wave function, they're the same thing.
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。
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。
So we do, in fact, have a dependence on what the Angle is of the electron as we define it in the orbital.
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