Let's try it with a different equation of state, that isn't quite as simple as the ideal gas case.

考虑一个不同的状态方程，这状态方程不像理想气体状态方程那么简单。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 化学原理课程节选

You know how pressure changes with temperature at constant volume if you know the equation of state.

如果你知道状态方程,知道在体积恒定的时压强如何随着温度变化。

麻省理工公开课 - 热力学与动力学课程节选

And the mathematics of that equation involved a double derivative in time of x 0 plus some constant times x equals zero with some constraints on it.

那个数学方程式,包括了x对时间的二阶导数,加上常数乘以x等于,还有一些限制条件。

麻省理工公开课 - 固态化学导论课程节选

I take the time and put it in the y equation and demand that the y I get, agrees with this y.

然后我把时间代入 y 的方程,令得到的 y 的表达式等于这一段的 y

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 博弈论课程节选

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。

麻省理工公开课 - 化学原理课程节选

So here I've written for the hydrogen atom that deceptively simple form of the Schrodinger equation, where we don't actually write out the Hamiltonian operator, but you remember that's a series of second derivatives, so we have a differential equation that were actually dealing with.

这里我写出了,氢原子薛定谔方程的,最简单形式，这里我们实际上,没有写出哈密顿算符,但是请记住那你有，一系列的二次导数,所有我们实际上会处理一个微分方程。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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