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Some people,for example, do this if they exercise hard during a heat wave.
VOA: special.2010.07.27
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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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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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That might seem confusing if you're thinking about particles, but remember we're talking about the wave-like nature of electrons.
如果你们把它想成是一个粒子的话是很矛盾的，但记住我们这里说的,是电子的波动性。
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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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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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Somebody try and wave their hands in the air if they know the answer.
谁知道答案,请举手回答一下
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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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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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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, if something cycles through five wavelengths in a single second, we would just say that the frequency of that wave is five per second.
如果一个东西在一秒,内经历了五个波长，我们就说这个波的,频率是每秒5次。
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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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So, for example, if we were looking at the actual wave function, we would say that these parts here have a positive amplitude, and in here we have a negative amplitude.
我们看，一个波函数,我们说，它这部分幅值，为正,这部分幅值为负，当我们看。
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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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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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So, if instead you put your particle somewhere down here on the electric field, or on the wave, the electric field will now be in the other direction so your particle will be pushed the other way.
还有方向，所以如果,你把粒子放在这下面，电场的方向相反,粒子会朝另一个方向运动。
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And you can think about that if you think about a standing wave, for example, where you can have amplitude at many different values of x, so an amplitude at many different distances, but you also have areas where there is a amplitude.
你们可以想象一下驻波，在不同ｘ处,可以有不同的振幅，在不同的距离有不同的振幅，但在某些地方振幅等于０．
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Because if we think about wave behavior of electrons and we're forming bonds, then what we have to do is have constructive interference of 2 different electrons, right, to form a bond, we want to and together those probabilities.
如果我们考虑,电子的波动行为,并且，我们要成键的话,我们要,把，这些概率，加在一起,如果。
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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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And when we're talking about the amplitude of the wave, we're talking about the deviation from that average level. So, if we define the average level as zero, you can have either a positive amplitude or a negative amplitude.
当我们讨论一个波的振幅时,我们说的是偏离平均位置的量,如果我们把平均位置,定义为零的话，那幅值不是,正的就是负的，有时候人们在。
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So, if we look at the bottom here and the actual plot of the wave function, we see it starts high, very positive, 0 and it goes down 0 and it eventually hits zero, and goes through zero 0 and then becomes negative 0 and then never quite hits zero again, although it approaches zero.
我们看,这下面这是波函数，我们看到它开始很高，是正的，然后降低直到,然后它穿过，变成负的,最后接近,但没达到，在这个。
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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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But in sigma orbitals, you have no nodal planes along the bond axis, so if we had a nodal plane here, we'd see an area where the wave function was equal to zero.
但在sigma轨道里，沿着轴向是没有节点平面的，如果我们有个节点，我们就会看到某个地方波函数等于0。
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So if we're talking about probability density that's the wave function squared.
如果我们要讨论概率密度,这是波函数的平方。
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You do not have to wave your hands in the air if you're math phobic, but since some of you are, let me just get you all to take a deep breath.
如果你有数学恐惧症你不必举手示意,既然有人是,那么让我们深呼吸一下
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So, also about Max Born, just to give you a little bit of a trivial pursuit type knowledge, he not only gave us this relationship between wave function squared, This is her grandfather, I don't know if you can see from the eyes, I feel like there's a little bit of a resemblance there.
这里有些，关于它的，花边新闻,他不仅带给我们，这个波函数平方的关系,还给我们带来了，他是她的外祖父，我不知道,你们能不能看出来，我觉得,他们眼睛长得很像。
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The more important thing that I want you to notice when you're looking at this wave equation for a 1 s h atom, is the fact that if you look at the angular component of the wave function, you'll notice that it's a constant.
我要你们注意的,更重要的一点是,当你们看到,这个氢原子1s轨道方程的时候，如果你们看,波函数，的角向部分，你们会发现它是一个常数。
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So if, in fact, we want to describe a wave function, we know that we need to describe it in terms of all three quantum numbers, and also as a function of our three positional factors, which are r, the radius, phi plus the two angles, theta and phi.
实际上，我们想描述波函数，我们知道我们需要,用这三个量子数来描述它，同样，波函数还是,三个位置变量的函数，它们是r半径，还有两个角度theta和。
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