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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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STUDENT: Right, we're going to do that in a second, but the answer is Fibonacci numbers, we define the first two.
学生：听不见：,我们马上会试一试，但是答案是斐波那契数列，我们可以定义下最初的两个数。
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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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But we can use equations that describe waves to describe matter, and that's what we're going to be doing today.
但我们可以用描述波的方程,来描述物质，这就是我们今天要做的。
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And in the inscription he writes, he boasts: "And the god Chemosh said to me, go, take Nebo from Israel.
他在题词中写到，他吹嘘到：,基摩神对我说，去，从以色列手中夺回尼波山。
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The first of these waves is, you remember, the restrictions on private property, even the abolition of private property.
第一波是，记得是什么吗，限制私产，甚至要废除私产制。
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And "home" is here made to rhyme with "Bapaume," bringing battlefront and home front together as a rhyme.
家乡“在这里是为了与“巴波姆“押韵“,将前线和后方放到一起成为一个押韵。
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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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Does anyone know the history of what Fibonacci was trying to do? Sorry, let me re-ask that. Fibonacci.
创始人是斐波纳契,有人知道斐波纳契想要干什么吗？抱歉，让我再问一次。
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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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We started talking about these on Wednesday, and what we're going to start with is considering specifically the wave functions for multi-electron atoms.
我们从周三开始讨论这些，而且我们将要以特别地考虑,多电子原子的波函数,为开始。
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It looks like just about everyone is able to go from the name of an orbital to the state function.
看来基本上大家都能从一个,给出的轨道名字得到它的波函数了。
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There are three waves, three waves of reform, so to speak, that will contribute to the creation of the city.
有三波改革，约略可以这么说，那会协助创建正义之城。
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Which actually is son of Bonacci which is the name of his father who was apparently a very friendly guy. First of all, does anyone know what a Fibonacci number is? Wow.
斐波纳契，它是波纳契的儿子,波纳契是它父亲的名字,听上去是个友好的男人不是吗,谁知道斐波纳契数列？
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And the reason I want to show you this is to notice that the recursion can be doubled.
如果我来写斐波那契数列你可以看看这儿,原因是我想让你看看这部分的递归可以翻倍。
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We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.
我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。
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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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But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.
波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。
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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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Each of these waves is regarded as in some way necessary for the proper construction of a just city.
每一波,在某些程度上,都被视为是真正建立正义之城的必需条件。
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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, regardless of the type of wave that we're talking about, there's some common definitions that we want to make sure that we're all able to use, and the first is amplitude.
所以，不管我们讨论的,是哪种波，它们都有一些我们,能用到的共同的定义,其中第一个就是幅值。
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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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And first we discussed the fact that well, in terms of a classical analogy, we don't really have one for wave function, we can't really think of a way to picture wave function thinking in classical terms.
首先我们说了，波函数没有一个，经典的类比，我们不能想象一个,经典的波函数的图像。
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Similarly, if we were to look at the radial probability distributions, what we would find is that there's an identical nodal structure.
相似地如果我们看看,径向概率分布,我们会发现有一个完全相同的波节结构。
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And on Monday what we were discussing was the solution to the Schrodinger equation for the wave function.
周一我们讨论了,薛定谔方程解的波函数。
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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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psi I mentioned that we can also solve for psi here, which is the wave function, and we're running a little short on time,
我说过我们也可以解,波函数，我们讲的稍微有点慢，
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