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The problem was that after successfully floating over one wave you find that there is another one behind it just as strong and ready to flood your boat.
VOA: special.2011.04.09
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Well, if this thing is going to vibrate for any length of time it better be a standing wave.
好的，如果它在任意时间振动,那它就是驻波。
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So certainly we would expect to see that it has an effect in terms of seeing its wave-like properties.
所以我们当然可以预期,会看到波动性质的效果。
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The Lady in Black looked at it. She remembered the wave of anger that had come over her when she had reached out her hand and silenced the clock that night three months before.
VOA: special.2010.05.15
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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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Supporters of the law say it will help fight a wave of crime blamed on illegal immigrants.
VOA: standard.2010.05.08
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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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But some experts say it could come back in a third wave early next year.
VOA: standard.2009.12.25
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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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"Or whether it is really even a wave." Hawkings says Democrats say there is no upcoming Republican "wave" which will sweep scores of them from office, pointing to a special election for the U.S.House seat for the late Congressman John Murtha of Pennsylvania.
VOA: standard.2010.05.19
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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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If de Broglie is correct, we could then model the electron in its orbit not moving as a particle, but let's model it as a wave.
如果德布罗意是对的，那么我们可以在电子轨道中建立电子模型,不是像粒子一样运动，而是像波一样运动。
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If a photon which has no mass can behave as a particle, does it follow then an electron which has mass can behave as a wave? 1920.
如果一个没有质量的光子,能像粒子一样运动，那么它能像一个,没有质量的电子那样以波的形式运动吗。
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And when we take the wave function and square it, that's going to be equal to the probability density of finding an electron at some point in your atom.
当我们把波函数平方时，就等于在某处,找到一个电子的概率密度。
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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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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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But when we're thinking about actual wave behavior of electrons, it's just important to keep in the back of our head that some areas have positive amplitude and some have negative.
电子的波动行为时,我们，要记住,某些地方是正的,某些地方是负的,当我们讲到。
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We can do the exact same thing when we talk about lithium, but now instead of breaking it up into two wave functions, we're breaking it up into three wave functions because we have three electrons.
在讨论锂时,我们也可以做，完全相同的事情,但不是把它分为两个波函数，而是分为三个波函数,因为我们有3个电子。
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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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It's going to be positive in terms of its wave function or in terms of its phase anywhere where y is positive.
只要ｙ大于零它的波函数,或者说是相位为正。
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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, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。
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No matter where you specify your electron is in terms of those two angles, it doesn't matter the angular part of your wave function is going to be the same.
不论你将，这两个角度,取成什么值，波函数的角向部分,都是，相同的。
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And what is plotted below is the actual wave function, so you can see it starts very high and then the decays down.
下面这画的是，波函数，你们可以看见它开始非常高,然后衰减下来。
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This is a table that's directly from your book, and what it's just showing is the wave function for a bunch of different orbitals.
这是一张你们书里的表格，它展示了各种,不同的轨道波函数。
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So, we can think about what is it that we would call the ground state wave function.
我们来考虑一下,基态的波函数，是怎么样的。
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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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