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For example, F x y z if I have an equation that looks like this, f of x, y, z.
打个比方，我有个这样的方程。
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So, for example, if we're to hold the time constant, this makes it a lot simpler of an equation, because what we can end up doing is actually crossing out this whole term here.
比如说，如果我们把时间,定为常数，这使得方程,大大简化，因为我们可以把,这一项划掉。
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This is going to be probably a homework at some point to do this. For now, let's take it for granted. Let's take it for granted that we know how to calculate this derivative from an equation of state like this.
这可能是将来的一个课后作业,现在，请把这当成理所当然的，理所当然地认为我们,知道怎样从一个状态,方程计算这样的微分式。
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The advantage of introducing that guy is that if you like, I can now write an equation for the acceleration as a vector.
引入它的好处是,如果你愿意的话,我可以把加速度写成矢量形式
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Good, so what I have here is an equation that tells me Player 1's best response for each possible choice of Player 2.
这个方程表示,参与人2不同策略下参与人1的最佳对策
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Well, the first thing you do is you write an equation.
嗯，第一点你要做的就是写一个方程。
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This is the equation that relates the expected return on an asset.
这个等式是关于某一资产的预期收益。
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And it turns out that the Schrodinger equation is an equation of motion in which you're describing a particle by describing it as a wave.
结果是薛定谔方程,用描述粒子波动性的方式,来描述这个粒子。
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So we can use an equation to relate the incident energy and the kinetic energy to the ionization energy, or the energy that's required to eject an electron.
因此我们可以用一个公式将入射能量,与动能和电离能，就是发射出一个电子所需要的能量关联起来。
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And the reason is, and this will come up on the problems and a lot of students end up using this equation, which is why I want to head it off and mention it ahead of time, we can't use an equation because this equation is very specific for light.
原因是，很多同学在解题时,都会用这个方程，所以我要,事先提醒你们一下,我们不能用这个方程，因为它只对光是用。
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Because this is what comes directly out of an equation of state, right?
因为它,可以直接从状态方程中得到？
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And again, this is something that comes from an equation of state.
我们再一次发现,这个可以从状态方程中得出。
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for real gases. This is an equation of state for an ideal gases.
我们需要描述实际气体,的状态方程。
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One is that he's just re-arranged an equation here and gotten both his PhD thesis and a Nobel Prize, but I think the more representative way to think about this is the real revolutionary idea that he put forth, which is that matter can actually behave as a wave.
一个是德布罗意仅仅,重新排列了一个方程,而且完成了博士论文并获得诺贝尔奖，但是我认为更具有代表性的观点,是他提出了实在的革命性的观点，那就是物质会有波的性质。
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So that's an equation of state.
所以它是态函数。
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We can't actually go ahead and derive this equation of the wave function squared, because no one ever derived it, it's just an interpretation, but it's an interpretation that works essentially perfectly.
从这个方程中,导出，波函数的平方，没有人可以这样做，这仅仅是一种解释，但这种解释，能解释的很好，自从它第一次被提出来之后。
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It's somewhat different when we're talking about the p or the d orbitals, and we won't go into the equation there, but this will give you an idea of what we're really talking about with this radial probability distribution.
当我们讨论ｐ轨道或者,ｄ轨道的时候会有些不同，我们那时不会给出方程，但它会给你们一个,关于径向概率,分布的概念。
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So, what we say here is we need to take a step back here and come up with an approximation that's going to allow us to think about using the Schrodinger equation when we're not just talking about hydrogen or one electron, but when we have these multi-electron atoms.
所有我们这里要说的是,我们需要退回一步,做一个近似,那样可以使我们用,薛定谔方程来考虑,让我们不是仅仅在讨论氢原子或者,一个电子的时候，而是多个电子的原子。
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c We know it's very specific for light because in this equation is c, the speed of light. So any time you go to use this equation, if you're trying to use it for an electron, just ask yourself first, does an electron travel at the speed of light?
我们知道它只对光适用是因为在这个方程里有,光速，所以下次你们用这个方程前，如果你们要把它用到一个电子上，先问问你自己，电子的运动速度是光速吗？
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This is called an equation of state.
这一状态方程把压强。
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When we first introduced the Schrodinger equation, what I told you was think of psi as being some representation of what an electron is.
当我们第一次介绍，薛定谔方程的时候，我说你们，可以,把psi看做是，电子位置的代表。
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Take these two equations, put an equal sign between them, replace this PR throughout with X, I'm going to have one equation and one unknown and that even the math phobics in the audience did in high school.
在这两个方程中间加个等号,将这里的Pr换成X,就会得到一个等式和一个未知数,剩下的问题,大家高中的时候就该回做了吧
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