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Suppose f of x, y, z equals k1, that is my equation, s1 and it gives me a solution s1.
假设我的方程是这样，然后给出了一个解。
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But when you solve the Schrodingerequation, you don't get just a set of solutions that are dependent upon one number.
但当你解薛定谔的方程式时，你没得到有一个统一答案的,一系列解决方法。
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So, we'll pick up with that, with some of the solutions and starting to talk about energies on Friday.
会去解薛定谔方程的某个方面，我们在周五,将从一些薛定谔方程的解开始。
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So you know from algebra I can't actually solve this. There may be multiple solutions to this. What would I have to do to change my code? And the answer is fortunately not a lot.
我解不出来方程,可能会有多组答案,我需要怎样修改我的代码呢？,很幸运的,答案是不用修改很多。
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Then, you go to the Math Department and say, "Please tell me what's the answer to this equation?"
然后,你到数学系去问,"请告诉我这个方程的解是什么"
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Just one strategy for each player and that strategy was given by this equation.
每个参与人只有一个策略,而那个策略是这个方程的解
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And, if we do so, we can actually get a handle on that Born exponent by solving the equation.
如果我们这样做，我们实际上能够得到波恩指数,通过解这个方程得到。
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You get a set of solutions that are dependent upon -These quantum states fall out of the solution to this equation.
你得到一系列的解,这些解依赖于量子状态,和方程解不相干的解。
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So, what we can do instead of talking about the ionization energy, z because that's one of our known quantities, so that we can find z effective.
我们做的事可以代替讨论电离能,因为那是我们知道的量子数之一，那是我们可以解出有效的，如果我们重新排列这个方程。
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And when you solved the relativistic form of the Schrodinger equation, what you end up with is that you can have two possible values for the magnetic spin quantum number.
当你们解相对论形式的,薛定谔方程，你们最后会得到两个,可能的自旋磁量子数的值。
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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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I am going to show the equation, but I don't expect you to solve it.
我将给出这个方程式，但我不期望你可以得出解。
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Set the intersection points equal, the equations equal to each other and solve.
令交点处的两个方程相等,然后就可以解出来了
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And on Monday what we were discussing was the solution to the Schrodinger equation for the wave function.
周一我们讨论了,薛定谔方程解的波函数。
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All right. So that's all I'm going to say today in terms of solving the energy part of the Schrodinger equation, so what we're really going to focus on is the other part of the Schrodinger equation, psi which is solving for psi.
好，今天关于薛定谔方程,能量部分的解，就讲这么多，我们今天真正要关注的,是另一部分，薛定谔方程，也就是解。
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And I am not going to take the time to solve it because I think that is a waste of class time, but those are the three unknowns.
但我并不打算把解这几个方程,我觉得那会是浪费课堂时间，但那是三个未知式。
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So if we want to solve for ionization energy, we can just rearrange this equation.
因此，要想解出电离能，我们只需要将这个方程中的项变换一下位置。
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And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.
此外，当我们解波函数,或者考虑薛定谔方程的结果时，我们看到的确３个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。
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psi The solution of the Schr?dinger equation is psi, a wavefunction.
那薛定谔方程的解是什么，是，一个波函数。
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Maybe you didn't realize that they are just simultaneous equations that you solve.
也许你并没有意识到,它们其实就是你们平时解的方程组
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Infinity is the force when we're thinking about it and our brains, negative infinity is when we actually plug it into the equation here, and the reason is the convention that the negative sign is just telling us the direction that the force is coming together instead of pushing apart.
说力有多大时，我们想到的,是无穷大，而方程解出来的,是负无穷，这是因为习惯上,我们用负号表示力的方向,是相互吸引而不是相互排斥的,所以我们可以用库仑定律。
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The basic idea in solving these equations and integrating is you find one answer, so then when you take enough derivatives, the function does what it's supposed to do.
解决这类方程以及积分的基本思想就是,你求出一个解,然后进行多次求导,求导的结果就满足条件
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So, all you will have the opportunity to solve differential equations in your math courses here. We won't do it in this chemistry course. In later chemistry courses, you'll also get to solve differential equations.
你们在数学课中有机会,遇到解微分方程,我们在这化学课里就不解了,在今后的化学课程里，你们也会遇到解微分方程的时候。
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The power of linearity is F=k1+k2 if I come across f of x, y, z equals k1 plus k2, if it is a linear equation, I don't have to go and solve it all over again.
线性的威力是,一个方程，如果它是个线性方程，那么我就不用再去解他了。
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You'd pull out your pencil and paper, you can do it as a matrix inversion if you know how to do that, or you can just simply do substitution of one equation into another to solve it.
你知道你在小学的时候是怎么做的对吧？,你拿出你的笔和纸,如果你会的话,你可以解一个方程组,或者你可以单纯地。
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That's when it hits the ground.
方程的解就是落地时间
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We don't have to worry about how you solve it, but it's problem in mathematics and the answer will be--surprise, it's going to be oscillating back and forth and that'll come out of the wash.
我们没必要去担心这个方程该怎么解,但这个数学问题的答案将会是令人惊讶的,弹簧会来回振荡,问题就迎刃而解了
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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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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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You won't have to solve it in this class, you can wait till you get to 18.03 to start solving these types of differential equations, and hopefully, you'll all want the pleasure of actually solving the Schrodinger equation at some point. So, just keep taking chemistry, 18 03 you'll already have had 18.03 by that point and you'll have the opportunity to do that.
你们不用在课堂上就解它，你们可以等到得到18，03之后,再开始解这些类型的微分方程，希望你们都想得到,实际解薛定谔方程的乐趣,所以，保持来上化学课，你们在那个点将会得到,你们有机会做到的。
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