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But he is not the only person in this equation,".
VOA: standard.2009.04.13
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And the solution to this equation looks like this where it is written in terms of a quantity called a wavefunction.
这个方程的解法是,看起来像是写成数学符号就是,波函数。
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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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In his words: "it illuminates part of the equation."
VOA: standard.2009.11.02
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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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For real gases, there's a whole bunch of equation the states that you can find in textbooks, and I'm just going to go through a few of them.
这是理想气体的状态方程,对实际气体,你可以在教科书里，找到许多描述它们的,状态方程。
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He was trying to describe electrons, but the theory said there are two roots in the quadratic equation and the second root is mathematically as interesting as the first one.
他当时只是想去描述电子,但是数学理论告诉我们,二次方程有两个根,而第二个根在数学上和第一个根一样有趣
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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
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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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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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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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So it's important to write out the equation you use, you need to write out the constants that you use to fill in that equation.
因此重要的是写出你所用的公式，你需写出,你用在公式中的常数。
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Now, the most interesting one for our class the equation of state that's the most interesting, is the Van der Waals equation of state, developed by Mr. Van der Waals in 1873.
由范德瓦尔斯在1873年发展起来,这个方程的美妙之处，在于它只需要两个参数，下面我们来研究一下。
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You realize it's very subtle, because the very first thing in that equation, which is m, has not yet been defined.
你会觉得这很微妙,因为方程里最基本的量 也就是 m,还没有人给它下定义
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But luckily for us, there's a classical equation of motion that will, in fact, describe how the electron and nucleus change position or change their radius as a function of time.
但幸运的是，有一个,经典方程描述了电子和核子,位置或者它们直接的距离是,如何随时间变化的。
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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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Minus p, right? But in fact, if you go back to the van der Waal's equation of state b here's RT over v minus b.
再减去p，对吗，但是实际上，如果你代回范德瓦尔斯气体的状态方程,这里是RT除以摩尔体积减去。
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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。
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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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That makes sense because we're losing energy, we're going to a level lower level, so we can give off that extra in the form of light. And we can actually write the equation for what we would expect the energy for the light to be.
这很合理，因为我们在损失能量,我们要到一个更低的能级去,我们要以光的形式给出额外的能量,我们可以写下光能量的方程。
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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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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
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Then we may, from this equation, say a certain force is acting in a given situation by multiplying the m times the a.
然后根据这个方程,我们就能说,得到给定条件下的作用力,它等于 m 和 a 的乘积
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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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c We know it's very specific for light because in this equation is c, the speed of light. So any time you go to use this equation, if you're trying to use it for an electron, just ask yourself first, does an electron travel at the speed of light?
我们知道它只对光适用是因为在这个方程里有,光速，所以下次你们用这个方程前，如果你们要把它用到一个电子上，先问问你自己，电子的运动速度是光速吗？
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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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So, essentially when we're talking about these equations up here, all we're doing is talking about the regular Rydberg formulas, but instead we could go back and re-derive the equation for any one electron atom, which would just mean that we put that z squared term in the front.
所以本质上,当我们讨论，这些问题时，我们说的是常规的，Rydberg公式，但对任何其他单电子原子，我们不用,从头再推到，而是仅仅把，z平方项放在前面。
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