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。

麻省理工公开课 - 固态化学导论课程节选

Now, it's also very useful to look at some of the relations that come out of these fundamental equations.

我们接下来可以考察,从这些基本方程中得出的一些方程。

麻省理工公开课 - 热力学与动力学课程节选

And thanks to our equation simplified here, it's very easy for us to figure out what actually the allowed energy levels are.

由于有了简化的方程，我们很容易看出,这些允许的能级在那里。

麻省理工公开课 - 化学原理课程节选

And what he does is writes this equation here.

他所做的就是写这些下方程式。

麻省理工公开课 - 固态化学导论课程节选

All it could do, though, was solve those equations.

它所能做的就是解决这些方程组问题。

麻省理工公开课 - 计算机科学及编程导论课程节选

So the equations are very smart.

这些方程真的很神奇

耶鲁公开课 - 基础物理课程节选

Well, then, we could just use that for our equation of state.

然后我们就可以把这些数据,作为我们的状态方程。

麻省理工公开课 - 热力学与动力学课程节选

And where do we find these things?

那么我们要在哪找到方程式中的这些量呢？

麻省理工公开课 - 固态化学导论课程节选

And that's why all those reactions, first of all, in some sense what I put up was kind of a trivial statement in actual fact saying they all happen spontaneously because I didn't specify what we were starting with exactly, what concentrations we were starting with.

首先这就是为什么所有的这些方程，在某种程度上,我举得这些例子说它们自发产生,这是一个琐碎的陈述,因为我没有说明，我们从什么地方开始。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

Just like u, we'd like to be able to express it in a way that allows us to calculate what happens only from equation of state data.

就像内能u一样，我们希望能够利用状态方程的数据,计算出其表达式,这些表达式能方便我们说出即将发生的过程。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 化学原理课程节选

And they're straightforward to derive.

推到这些方程也非常直接。

麻省理工公开课 - 热力学与动力学课程节选

And the useful outcome of all that is that p we get to see how entropy changes with one of those variables in terms of only V, T, and p, which come out of some equation of state.

这样做的重要结果是,我们得到了熵随着V，T或者,其中一个变量变化的情况，这些可以从状态方程得到。

麻省理工公开课 - 热力学与动力学课程节选

I just go through these equations, 3 but be careful to Z equals three.

我只检查这些方程式，但是注意了，Z等于。

麻省理工公开课 - 固态化学导论课程节选