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But luckily for us, there's a classical equation of motion that will, in fact, describe how the electron and nucleus change position or change their radius as a function of time.
但幸运的是，有一个,经典方程描述了电子和核子,位置或者它们直接的距离是,如何随时间变化的。
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We're going to be looking at the solutions to the Schrodinger equation for a hydrogen atom, and specifically we'll be looking at the binding energy of the electron to the nucleus.
我们将研究下氢原子薛定谔方程的解,特别是电子和核子的结合能,我们将研究这部分。
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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。
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And so, the radial probability density at the nucleus is going to be zero, even though we know the probability density at the nucleus is very high, that's actually where is the highest.
所以径向概率密度,在核子处等于零，虽然我们知道在，核子处概率密度很大,实际上在这里是最大的，这是因为。
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So, essentially we're just breaking it up into two parts that can be separated, and the part that is only dealing with the radius, so it's only a function of the radius of the electron from the nucleus.
所以本质上我们把它写成,两个可分离的部分，这部分，只与半径有关，它仅仅是，电子,到核子距离的函数。
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And if we go ahead and square that, then what we get is a probability density, and specifically it's the probability of finding an electron in a certain small defined volume away from the nucleus.
我们得到的是，一个概率密度，它是，在核子周围，某个很小的,特定区域,找到电子的概率,所以它是概率密度。
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So this squared at the origin is going to be a very high probability, and it decays off as you get farther and farther away from the nucleus or from the center, and that's independent of the angle.
所以这个平方,在原点处非常高，随着离核子的距离,越来越远,它逐渐衰减，并且它和角度是没有关系的。
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So all that Bohr, for example, had to go on at this point was a more classical picture of the atom, as you can see on the left side of the screen there, which is the idea that the electrons orbiting the nucleus.
原子的经典图像，你们可以,看到屏幕左边，这是电子，绕着核子旋转，的概念,他已经知道。
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That's a deterministic way of doing things, that's what you get from classical mechanics.
与核子的半径,是从经典力学中得到的，但我们从量子力学模型，知道的事实是。
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So, we now have this new way of thinking about how a nucleus and an electron can hang together, and this is quantum mechanics, and we can use this to come up with a new way to describe our atom and the behavior of atoms.
我们现在有了这种全新的,方法来研究电子和核子是,如何在一起的，这就是，量子力学，通过它我们,可以用一种全新的方式。
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We've got a lot of constants in this solution to the hydrogen atom, and we know what most of these mean. But remember that this whole term in green here is what is going to be equal to that binding energy between the nucleus of a hydrogen atom and the electron.
在这个解中有很多常数,其中大部分我们,都知道它们代表的意思,但记住是这整个绿色的部分,等于核子和电子的结合能。
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The reason in our radial probability distributions we start -- the reason, if you look at the zero point on the radius that we start at zero is because we're multiplying the probability density by some volume, and when we're not anywhere 0 from the nucleus, that volume is defined as zero.
在径向概率密度里，我们开始,如果你们看半径的零点，我们从零点开始,因为我们用概率密,度乘以体积,而当我们，在离核子很近的地方,体积是，所以我们会在这里。
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