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Electromagnetic energy travels almost like an ocean wave - up and down,up and down.
VOA: special.2010.12.08
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He came up with the relationship that nu bar, which is called wave number --He found the reciprocal.
他也提出了它们与波数的关系，波数是波长的倒数。
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We need to come up with an experiment in which the electron is going to be forced to behave as a wave.
我们得想出个实验,在这个实验中电子必须,要表现得像波一样。
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A mighty wave rose up and over the side of the boat.
VOA: special.2009.02.28
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So when you operate on the wave function, what you end up with is getting the binding energy of the electron, and the wave function back out.
所以当你将它作用于波函数时，你得到的是电子的结合能,和后面的波函数。
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"It is going to be a big anti-incumbent year, and a big anti-Washington year, and what is still left a little bit up in the air after last night is how much that anti-incumbent wave, how disproportionately that anti-incumbent wave, will wash over the Democrats."
VOA: standard.2010.05.19
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If you hook a radio wave up with a radio, you can tell the radio wave was there because what the radio is doing?
如果你用收音机检测无线电波，你可以知道无线电波在那,因为收音机在干什么？
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Keep them up. Wave them in the air with a bit of motion.
先别放下手,再举一小会
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There is a story that near the end of his life, Aristotle was himself brought up on capital charges, as was Socrates, due to another wave of hostility to philosophy.
而在他快临终时有个故事讲到，亚里士多德,遭到死刑控告，如同苏格拉底一般，因为另一波的反哲学斗争。
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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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Think about that. All this, Comus explains : Nay Lady, sit; if I but wave this wand, Your nerves are all chained up in Alabaster, And you a statue; or as Daphne was, Root-bound that fled Apollo.
试想一下，所以这一切，Comus解释到：,小姐，坐，但如果我挥舞这个棒子，你的所有神经都束缚在这个大理岩上了，你是一尊雕像，或像月桂树那样，被绑在根上逃往阿波罗。
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If we overlay what the actual molecular orbital is on top of it, what you see is that in the center you end up cancelling out the wave function entirely.
如果我们把真实的分子轨道覆盖在上面，你可以看到中间的,波函数是完全抵消掉了。
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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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So, having other particles around that have the same energy that you could technically add up if you were adding them up like a wave, you can't do the same thing with particles, they're all separate.
所以，如果它们是波,你可以把其他的,拥有相同能量的粒子加起来，但是你不能把这些粒子加起来，因为它们是分离的。
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while we do, in fact, have the wave function plots up here.
这里已经画了波函数，但看这些图时一个关键的地方。
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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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So instead, these would be canceling out wave functions between the two, so we would end up with a nodal plane down the center.
相反，两者之间的,波函数会相互抵消，所以我们在中间会得到一个节面。
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So, as an example, let's take argon, I've written up the electron configuration here, and let's think about what some of the similarities might be between wave functions in argon and wave functions for hydrogen.
所以作为一个例子我们来看看氩，我已经把它的电子构型写在这里，我们来考虑氩和,氢波函数之间的,一些相似性。
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sigma1s And what we end up for our molecular wave function is sigma 1 s.
最后我们得到了分子波函数。
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I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
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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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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, remember we can break up the total wave function into the radial part and the angular part.
记住我们可以把整体波函数,分解成径向部分和角向部分。
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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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sb So in this case we would have 1 s a and 1 s b, and instead we would subtract one from the other, and what we would see is that instead of having additional, more wave function in the middle here, we've actually cancelled out the wave function and we end up with a node.
在这种情况下我们有1sa和，两者相减，我们可以看到不是在，中间有了额外更多的波函数，而是我们消掉了,波函数得到一个节点。
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So, if you're woken up during slow-wave sleep you're going to be thinking "Did I take the-- yes, while I was dreaming I was thinking about the garbage," but if you're woken up during REM, "But a monkey was eating my grandmother," and that sort of thing. So, there is a distinction.
在慢波睡眠中醒过来,你会想“我倒垃圾了吗？,原来我睡觉是想着倒垃圾了”,但如果你在REM睡眠中醒过来，“天啊，有只猴子在吃我奶奶”,这就是真正的梦和半睡半醒的想法之间的区别。
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