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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, 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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The perspective is tricky-- and so we're trying to find the roots.
从视图上来看可能比较困难,因此我们来试试找到这个问题的解。
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So, so far, we've been working pretty hard and we haven't, I guess, learned a lot, we've just kind of solved the thing out.
到目前为止我们的计算真的很繁琐,但是我觉得我们没学到什么东西呢,我们只是解出了一道题罢了
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I'm going to shift and spend the rest of this class on a couple of mysteries.
本节课接下来的时间,我们来讲几个心理学未解之谜。
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So always amazing to us how we go into the problem, our eye or mind can see one class of solutions, but the math will tell you sometimes there are new solutions and you've got to respect it and understand and interpret the unwanted solutions, and this is a simple example where you can follow what the meaning of the second solution is.
解决问题的方式总能让人惊喜不已,我们的眼睛或思想可以看见一类解,但数学有时会告诉你还有新的解,你不能忽视它,而是解释这些不期而至的解,这只是一个简单的例子,由此你可以理解第二个解的意义
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Let me just solve this for--let's solve x1 for r.
现在我们先解出用r表示x1的关系等式。
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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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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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We looked at the wave functions, we know the other part of solving the Schrodinger equation is to solve for the binding energy of electrons to the nucleus, so let's take a look at those.
我们看过波函数，我们知道解,薛定谔方程的其他部分,就是解对于原子核的电子结合能，所以我们来看一看。
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psi I mentioned that we can also solve for psi here, which is the wave function, and we're running a little short on time,
我说过我们也可以解,波函数，我们讲的稍微有点慢，
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Somebody who's not a math major, tell me how I solve out for the maybe the math majors can't do it actually, it's too simple.
谁不是数学专业的,告诉我们怎么解呀,数学专业的觉得它太简单而不屑去解
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We'll be using the solutions, so you shouldn't have a problem, but I wanted to point it out so it does not look too strange to you.
我们将会用它的解，所以你们不应该问题，但是我想提出它,这样你们就不会对它太陌生。
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So you can see that we're starting to have a very complicated equation, and it turns out that it's mathematically impossible to even solve the exact Schrodinger equation as we move up to higher numbers of electrons.
所有你们可以看到我们得到了,一个非常复杂的方程，结果是它在数学上是,不可能解出确定的,薛定谔方程,当我们考虑更高的电子数目的时候。
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We don't always want to go and solve the Schrodinger equation, and in fact, once we start talking about molecules, I can imagine none of you, as much as you love math or physics, want to be trying to solve this Schrodinger equation in that case either. So, what Lewis structures allow us to do is over 90% of the time be correct in terms of figuring out what the electron configuration is.
我们并不想每次都去解薛定谔方程，而且实际上，一旦我们开始讨论分子，我可以想象,你们中没有一个人，不管你有多么热爱数学或物理，会想去解这种情况下的薛定谔方程,总之，路易斯结构能让我们,有超过，90%，的概率判断出正确的,电子排布。
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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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So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。
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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 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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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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So the correct answer for titanium plus two Ar3d2 is going to be argon 3 d 2, whereas if we did not rearrange our order here 4s2 we might have been tempted to write as 4 s 2 so keep that in mind when you're doing the positive ions of corresponding atoms.
所以正2价钛离子,的正确答案是，然而如果我们不重新安排顺序,我们可能会写出2,所以请记住,它当你们在解关于原子,的正离子的时候。
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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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Good, so this is our key expression and I'm going to use this expression; I'm going to solve it for q1.
好了,这是个关键表达式,我们一会还要用到它的,我们用它来解出q1
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So, for example, if we needed to figure out the electron configuration for titanium, 4s2 it would just be argon then 4 s 2, 3d2 and then we would fill in the 3 d 2.
所以举个例子,如果我们需要解出钛的电子构型，它会是Ar然后，然后我们填充。
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But, as I said before that, we have some more quantum numbers, when you solve the Schrodinger equation for psi, these quantum numbers have to be defined.
但我说了，我们还有，其它的量子数，当你解，psi的薛定谔方程时，必须要，定义这些量子数。
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It tells me that the best response to S2 is the ?1 that solves this equation, that solves this first order condition.
我们得出S2的最佳对策是?1,?1是这个方程的解,它满足一阶条件
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psi So we're going to for psi, and before that, we're going to figure out that instead of n just that one quantum number n, we're going to have a few other quantum numbers that fall out of solving the Schrodinger equation for what psi is.
我们要讲到，但在这之前，我们已经知道了,主量子数，现在我们需要知道，其他一些,解psi的薛定谔方程,所需要的量子数。
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What we can actually do is we could solve out for the X and for the Y.
实际上我们能够解出X和Y的值
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So we know that we can relate to z effective to the actual energy level of each of those orbitals, and we can do that using this equation here where it's negative z effective squared r h over n squared, we're going to see that again and again.
我们知道我们可以将有效电荷量与,每个轨道的实际能级联系起来，我们可以使用方程去解它,乘以RH除以n的平方,它等于负的有效电荷量的平方,我们将会一次又一次的看到它。
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