How far you are away from the nucleus in terms of a radius, they don't depend at all on those two angles, theta they're independent of theta phi and they're independent of phi.

只和离核子的距离，也就是半径有关，它们和,另外两个角度无关，它们不决定于,也不决定于。

麻省理工公开课 - 化学原理课程节选

theta And, I'm going to abbreviate, just put theta.

简而言之，输入角。

麻省理工公开课 - 固态化学导论课程节选

And similarly, actually, if we're looking at our polar coordinates here, what we see is it's any place where theta is equal to is what's going to put up on the x-y plane.

类似的，如果我们,看这里的极坐标系，我们能看到只要在theta等于,多少的地方就是ｘｙ平面。

麻省理工公开课 - 化学原理课程节选

So we have the operationon the wave function in terms of r, theta, and phi and remember this e is just our binding energy for the electron, and we get back out this wave function.

我们用r，θ，φ来表示,将算符作用于波函数,而且记住e仅仅是电子结合能，然后后面加上波函数。

麻省理工公开课 - 化学原理课程节选

You can also have angular notes, and when we talk about an anglar node, what we're talking about is values of theta or values of phi at which the wave function, and therefore, the wave function squared, or the probability density are going to be equal to zero.

我们也可以有角向节点，当我们说道一个角向节点时，我们指的是在某个theta的值,或者phi的值的地方，波函数以及波函数的平方，或者概率密度等于零。

麻省理工公开课 - 化学原理课程节选

It doesn't depend on theta, it doesn't depend on phi.

它和theta无关，和phi也无关。

麻省理工公开课 - 化学原理课程节选

On what else do you use theta for, if not angles?

如果不用angles的话，你会用些什么词去描述角度呢？

麻省理工公开课 - 固态化学导论课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

So if, in fact, we want to describe a wave function, we know that we need to describe it in terms of all three quantum numbers, and also as a function of our three positional factors, which are r, the radius, phi plus the two angles, theta and phi.

实际上，我们想描述波函数，我们知道我们需要,用这三个量子数来描述它，同样，波函数还是,三个位置变量的函数，它们是r半径，还有两个角度theta和。

麻省理工公开课 - 化学原理课程节选