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And we can actually better visualize this if we plot how that energy changes as a function of internuclear distance.
而我们就能更清楚地看到这些，如果我们画出,能量随核间距的变化曲线。
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In other words, now I know how to tell how the Helmholtz free energy changes as a function of temperature.
换句话说，我现在知道如何写出亥姆赫兹,自由能作为温度的函数。
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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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You can see low voltage, low energy, high voltage, high energy. It is a linear function.
你会看到，低电压，低能量，高电压，高能量，这是种线性关系。
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You know, we've done a bunch of thermochemistry, and we've kind of seen that the energy of mixing, your energetics don't change too much as a function of temperature.
我们做过很多的化学热力学习题，某种程度上我们发现混合的能量，并不随着能量,发生大的改变。
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OK, now, we're going to look at the internal energy, and we're going to pretend that it is explicitly a function of temperature and volume.
好，我们接下来看看内能，我们假设,它是温度和体积的函数。
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But it's allowed to say the internal energy is a function of temperature and volume.
但是我们也可以说内能,是温度和体积的函数。
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- The same place is that energy is a function of these four quantum numbers.
它就是这个结论,能量是这四个量子数的机能显示。
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So, we do this here for the photoelectric effect, and in terms of the photoelectric effect, what we know the important point is that the incoming photon has to be equal or greater in energy then the work function of the metal.
所以，我们做这个是为了说明，光电效应，在光电效应方面，我们知道的最重要的事情,就是入射的光子能量必须等于,或者大于金属的功函数。
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I want to plot energy in the system as a function of interatomic spacing.
我想把这个系统中的能量,按照原子间距来划分。
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We can also talk about it in terms of if we want to solve, if we, for example, we want to find out what that initial energy was, we can just rearrange our equation, or we can look at this here where the initial energy is equal to kinetic energy plus the work function.
初始能量是多少，也可以,写成另一种形式,我们可以把方程变形,或者我们看这里,初始能量等于,动能加功函数。
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Lowest energy to highest energy and it is a function of occupancy.
从最低能量到级最高能量级都是这样,而这是占据的函数。
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So, if we look at this graph where what we're charting is the internuclear distance, so the distance between these two hydrogen atoms, as a function of energy, -- what we are going to see is a curve that looks like this -- this is the general curve that you'll see for any covalent bond, and we'll explain where that comes from in a minute.
因此，如果我们来看一看这幅曲线图,这里我们画的横坐标是核间距，也就是这两个氢原子之间的距离，纵坐标是能量，我们看到的这是能量关于核间距的曲线-,这是一条普遍的曲线，在研究任何共价键时你都会遇到，我们马上就会解释一下它是怎么来的。
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now we're not just talking about 1 photon, 1/2 let's say we shoot them all at the same time at our metal, each of them having some energy that's let's say 1/2 the work function. So, just to take a little bit of an informal survey, who thinks here that we will have an electron that is ejected in this case?
我们现在不仅仅讨论一个光子，它们所具有的能量是功函数的，我们在同一时刻把它们打到金属上,我们做一个不太正式的调查,谁认为这种情况下,一个电子会被打出？
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We'll then look at the quantity, internal energy, which we define through the first law, and we think of it as a function of two variables T and V.
接下来我们考虑内能，这是由热力学第一定律定义的物理量，我们把它看作T和V的函数。
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So, now we can talk about it in different terms, Ei for example, talking about e sub i, which is the incident energy or the energy of the light that comes in, or talking about work function here, and that's just another way to say threshold energy.
现在我们可以从不同的方面,来谈论它了，举例来说，它是入射能量或者进来的光的能量,或者谈论这里的功函数，它是另一种描述临界能量的方式。
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So, therefore, we can rewrite our equation in two ways. One is just talking about it in terms only of energy where our kinetic energy here is going to be equal to the total energy going in -- the energy initial minus this energy of the work function here.
所以我们可以把方程,写成两种形式，一个是,只考虑能量，动能等于总的,入射能量-初始能量减去,功函数的能量，我们如果想解决,比方说，我们想知道。
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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。
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