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And if it is going to be a standing wave then this must be an integral number of wavelengths.
如果这有个驻波的话,那么周长就是个整数。
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So this validates de Broglie and it also validates the whole concept of wave-particle duality.
这就证实了德布罗意的观点,也证实了,波粒二象性的原理。
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In contrast, if we're taking the wave function and describing it in terms of n, l, m sub l, and now also, the spin, what are we describing here?
相反，如果我们考虑一个波函数,然后用ｎ，ｌ，ｍ小标ｌ,还有自旋，我们描述的是什么？
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It seems to depict a storm at sea, almost as if the Egyptians are in boats, and a big wind makes a giant wave, and another wind then makes it crash down on them.
而是描述了一阵风，就像埃及士兵在船上,狂风掀起大浪，另一阵风，掀翻了船。
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It' s very, very difficult to chase after a wave.
追随潮流是件相当困难的事。
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It doesn't mean that they grew up south of the Mason-Dixon Line or wave a certain kind of flag or--but the older term for it was "stooge."
那不意味着,他们成长于梅森—狄克森线以南,挥动某种旗帜,或者-但是更广泛是“stooge“表示助手“
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And an electron is something where, i n fact, we might be able to, if we calculate it and see how that works out, actually observe some of its wave-like properties.
如果我们对电子做计算,并且知道如何算出来的,那么我们是可以观测到,电子的一些波动性质的。
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Other times it behaves as a wave, and that is the way it helps us to think and rationalize what we observe.
另一些时候它更像波，而这是能帮助我们思考,和理解我们所观察到的东西的一种方法。
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We can't actually go ahead and derive this equation of the wave function squared, because no one ever derived it, it's just an interpretation, but it's an interpretation that works essentially perfectly.
从这个方程中,导出，波函数的平方，没有人可以这样做，这仅仅是一种解释，但这种解释，能解释的很好，自从它第一次被提出来之后。
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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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If a proton which has no mass can behave as a particle does it follow that an electron which has mass can behave as a wave?
如果一个没质量的光子能像粒子一样,具有质量的电子能否,表现得像波一样吗？
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So, at this place where it hits zero, 0 that means that the square of the wave function is also going to be zero, right.
它达到0的地方，这意味着波函数的，平方也是,如果我们看概率密度图。
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So, remember this makes sense if you just think of it as a wave and forget the particle part of it for right now, because that would be very upsetting to think about and that's not, in fact, what's going on, we're talking about quantum mechanics here.
记住如果你们把它看做是一个波,而忘记它是一个粒子时，这就是可以理解的了，因为如果把它看做,一个粒子就行不通了，实际上也不是这样的，这里我们是以量子力学的角度来考虑问题。
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Alright. So, since we have these terms defined, we know the frequency and the wavelength, it turns out we can also think about the speed of the wave, and specifically of a light wave, and speed and is just equal to the distance that's traveled divided by the time the elapsed.
好了，我们已经定义了，这些术语，我们知道了，频率和波长，现在可以来考虑,波的速度了，特别是光波的速度，速度等于它走过的距离,除以所用的时间，因为我们。
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So again, if we think of a graph of the wave function, we had the wave function is at its highest amplitude when it's lined up with the nucleus, and then as we got further away from the nucleus, the amplitude of the wave function ends up tapering off until it never hits zero exactly, but it goes down very low.
同样，如果我们想象一幅波函数的图，波函数在原子核的位置上,有着最高的振幅，随着与原子核距离变远，波函数振幅逐渐变小直到,它永远不会到零，但它会变得很小。
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And what here is just a graph of the 1 s wave function going across some radius defined this way, and you can see that the probability - well, this is the wave function, so we would have to square it and think about the probability.
这里是,1s波函数,沿这个方向的图，你们可以看到概率,这是波函数，所以我们可以把它平方,并想成是概率。
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So we can draw that for 1 s a, we can also draw it for 1 s b, and what I'm saying for the molecular wave function is that we have the interference between the two, and we have a constructive interference, so we end up adding these two wave functions together.
所以我们可以对1sa画出它来，我们也可以对1sb画出它来，对于分子波函数我要说的是,它们两者之间会干涉，这里我们有相长干涉，所以我们得到的是波两个波函数加起来。
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So we can do this essentially for any atom we want, we just have more and more wave functions that we're breaking it up to as we get to more and more electrons.
所以我们基本上对，任何一个原子都可以这么做,我们仅仅会有越来越多的波函数,因为我们将它分为越来越多的电子。
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psi1 0 0 We can call that psi 1, 0, 0, is how we write it as a wave function.
我们可以叫它，这是我们作为波函数的形式写出它。
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So, I don't know what she grew up hearing about when she went to her grandparents' house, but it might have been wave function squared.
我不知道她小时候,在，她外祖父家里，听到了什么，也许她听到过，波函数。
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It's the same thing with molecules a molecular wave function just means a molecular orbital.
这对于分子也是一样,分子波函数就意味着分子轨道。
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It is in a standing wave configuration.
是个驻波结构。
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So, what we can do to actually get a probability instead of a probability density that we're talking about is to take the wave function squared, which we know is probability density, and multiply it by the volume of that very, very thin spherical shell that we're talking about at distance r.
我们能得到一个概率,而不是概率密度的方法,就是取波函数的平方，也就是概率密度，然后把它乘以一个在ｒ处的,非常非常小的,壳层体积。
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So, it turns out that n is not the only quantum number needed to describe a wave function, however. There's two more you can see come out of it.
事实上，n不是描述一个波函数需要的,唯一的量子数，你们可以看到，还需要，两个量子数。
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Similarly, with the second hydrogen atom, we've got the nucleus in the middle, and the 1 s b wave function around it.
类似的，在第二个氢原子里面，我们在中间有原子核，周围有1sb波函数。
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