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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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The electronic configuration, all it is is the shorthand notation for that one electron approximation for the Schrodinger equation for lithium.
电子构型就是，对于锂的薛定谔方程,的单电子近似的,简化形式。
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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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The second thing is, just as in the case of the violin string, the wave equation, as posed by Schrodinger, has a plurality of solutions.
第二，就那个小提琴弦而言，波动方程，被薛定谔所提出的，有许多解法。
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All right, so that's what we're going to cover in terms of the energy portion of the Schrodinger equation.
好，这就是我们要讲的,关于薛定谔方程能量的部分。
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The Schr?dinger equation will give us the energy levels in molecules.
薛定谔方程会告诉我们,分子中的能级。
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Also, when we're looking at the Schrodinger equation, it allows us to explain a stable hydrogen atom, which is something that classical mechanics did not allow us to do.
当我们看一个薛定谔方程的时候，它给出一个稳定的氢原子,这是在经典力学中做不到的。
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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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Schrodinger said I am going to take that same idea, and I am going to apply it to a larger scale system.
薛定谔说我将用同样的思路，我要把它用到一个更大的系统中。
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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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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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And this is Erwin Schrodinger, and this is the equation that he put forth where we have hat psi being equal to e psi.
这就是埃尔文？薛定谔，在这个方程中,他提出,所以，让我们来解释一下。
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If you look in your book there's a whole table of different solutions to the Schrodinger equation for several different wave functions.
如果你们看书的话,上面有一整张,许多，不同波函数,薛定谔方程解的表。
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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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And the thing about what Schrodinger did was all he imposed on a system was the electron behaves as a wave and is bound.
薛定谔所做的,是建立在一个系统之上,电子是像波一样运动的并且是有界限的。
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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 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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And what we can do is we can also use the Schrodinger equation to make these accurate predictions for any other atom that we want to talk about in the periodic table.
我们能做的是,我们可以使用,薛定谔方程去做一些,关于我们想要讨论的元素周期表,中任何一个原子的预测。
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We saw the Schr?dinger equation for atomic hydrogen, but you can write it for more complex systems.
我们看过原子氢的薛定谔方程，但其实我们能把他用在更复杂的体系。
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The one problem that we run into is as we go to more and more atoms on the table, as we add on electrons, the Schrodinger equation is going to get more complicated.
我们将会遇到的一个问题,是当我们处理周期表中越来越多的原子时，当我们增加了电子，薛定谔方程,变得愈加复杂。
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Erwin Schrodinger also an Austrian.
埃文，薛定谔也是澳大利亚人。
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De Broglie, Heisenberg and Schrodinger.
德布罗意，海森堡和薛定谔。
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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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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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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。
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This is the same equation, the Schr?dinger equation, only it has different boundary conditions.
相同的方程，薛定谔方程，只不过有不同的限制条件。
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After that, we'll move on to matter as a wave, and then the Schrodinger equation, which is actually a wave equation that describes the behavior of particles by taking into account the fact that matter also has these wave-like properties.
之后，我们会转移到物质，是一种波的话题和薛定谔方程，薛定谔方程是描述粒子,在考虑物质的波动性质后,的行为的方程。
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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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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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