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But we can use equations that describe waves to describe matter, and that's what we're going to be doing today.
但我们可以用描述波的方程,来描述物质，这就是我们今天要做的。
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And if your answer is no, your answer will be no, then you just know you can't use this equation here.
如果不是，那就不能，你就知道，你不能用这个方程了。
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I know I only need 2, so I can relate dV dV to dp through the ideal gas law.
我只需要两个就够了，因此可以用,理想气体状态方程消去。
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We have two, well, let me draw this is as a square.
我们现在又两个，让我用方程式写出来。
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System of linear equations. What are the equations here? Well, I could say, you know, the number of pigs plus the number of 20 chickens equals 20, right? Because we've got 20 heads. And then what else do I have?
如何解决这个问题呢？,用线性方程式的办法来解决，等式是什么呢？你应该知道,猪的数量加鸡的数量等于,对吧？因为我们有20个头？
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Do you realize that this is a pair of simultaneous equations in which you can solve for these two unknowns, if you like, in terms of these two knowns and these coefficients, which are like these numbers, 3, 2, 4, and 6?
你们是否发现这其实就是一个方程组,你可以用它来解出这两个未知量,你愿意的话,可以用这两个已知量,和这些系数,比如这些数字,3,2,4和6
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So prices are determined as follows: prices depend on some parameters I'm just going to call a and b, and let me write the equation and then we'll see what it looks like.
价格由如下因素决定,价格取决于两个参数a和b,我们用方程写一下吧
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All right. So jumping in to having established that, yes, particles have wave-like behavior, even though no, hey're not actually photons, we can't use that equation.
好的，我们已经承认了，粒子有波动性，虽然它们不是光子，我们不能用这个方程。
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You can go ahead and use that equation, or you could figure it out every time, because if you know the total number of nodes, and you know the angular node number, then you know how many nodes you're going to have left.
你们可以直接用这个方程，或者每次都自己算出来，因为如果你们知道了总的节点数，又知道角向节点数，就知道剩下的节点数是多少。
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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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We are getting these by plotting the values from the Schrodinger equation.
我们标注薛定谔方程的值时,也用到了这个。
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In terms of the Schrodinger equation, we now can write it in terms of our polar coordinates here.
在薛定谔方程中，我们现在可以用,极坐标的方式来表示了。
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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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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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So, we just want to appreciate that what we'll be using in this class is, in fact, the solutions to the Schrodinger equation, and just so you can be fully thankful for not having to necessarily solve these as we jump into the solutions and just knowing that they're out there and you'll get to solve it at some point, hopefully, in your careers.
所以，我们仅仅想要鉴别,将会在这门课中用到的，事实上就是薛定谔方程的解，而且你们可以非常欣慰,因为你们没有必要去,解这些方程而是直接用它们的解,并且知道这些解出自那里,希望你们在学习生涯中。
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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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So, we can do that by using this equation, which is for s orbitals is going to be equal to dr 4 pi r squared times the wave function squared, d r.
用这个方程,对于s轨道，径向概率分布,4πr的平方,乘以波函数的平方,这很容易理解。
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In addition to that, we have that epsilon nought value, remember that's the permittivity constant in a vacuum, and basically that is what we use as a conversion factor to get from units. We don't want namely coulombs to units, we want that will allow us to cancel out in this equation.
这是电子的电荷，此外，我们有epsilon零，记住这是真空的介电常数，这是我们用来转换单位的转换常数,我们不想用库伦单位，我们希望这个可以在方程中约去它。
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