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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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So kind of that strange cursive r, and our n final is 2, R so 1 over 2 squared minus n initial, so 1 over 3 squared.
因为我们可以在这里用到它，这个有点奇怪的花体。
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One over two squared minus one over n squared 3 4 5 where n takes values three, four, five, six.
除以，2，的平方再减去1除以n的平方,将n赋值为。
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And I have this, to write it out, this is order the length of the list squared, OK?
我得写下来,这是把列表的长度平方，对么？
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To get the best fitting line, you find the line that minimizes the sum of squared distances.
要找到最切合的直线,就是要使,这些距离的平方和最小
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They're invariably cited as among the most beautiful and exquisite lines in Paradise Lost but on some level they've proven the bane of scholars because they can't be squared with any of the poem's theological message.
它们被单调地引证为,中最美最细致的诗句,但在某些层面他们证明了学者的祸害,因为它们并不能与诗歌所传达的神学信息相一致。
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pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
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So, the way to measure force is in kilogram meters per second squared.
所以,力的单位是千克米每秒平方
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They tell you precisely what the gases were, what the characteristics of those gases were, and it squared beautifully with all details that we heard about the Delphic Oracle.
他们会准确地告诉你,此为何种气体,以及该气体有何特性,而且它与我们所知的德尔菲神谕的,所有细节都相符合
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Like what the heck have we been spending our time for-- our time on with Bubble Sort and with Selection Sort and in fact there's plenty of other N squared sorts that we're not even gonna bother looking at.
真见鬼，我们竟然在-,冒泡排序和选择排序上花时间,而事实上，还有很多我们根本都不想考虑的,复杂度为N平方的排序方法。
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And the person we have to thank for actually giving us this more concrete way to think about what a wave function squared is is Max Born here.
需要感谢，马克思，波恩,给了我们，这个波函数平方的,具体解释，事实上。
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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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So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.
如果我们要讨论它的体积，我们要用的是表面面积，也就是４πｒ的平方，乘以厚度ｄｒ
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This depiction of matter takes you right up to E=MC E=MC And, that's all he had to work with for data.
物质的叙述，让我们一直等到,的平方，天才。，squared。，Brilliant。,那是他研究数据所得出的成果。
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I want to then do, I need to find the square root b squared plus h squared, right?
我接下来要求b的平方和h的平方,的和的平方根对不对？
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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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If it moves a lot--either way from the mean-- then this number squared is a big number.
如果距离均值的变动很大,那么这个平方数也会很大
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And we plug in our values and end up with mv squared mv^2/r-Ze^2/ over r minus Ze squared over And I am going to call this equation two.
我们最后的结果,就是,我把这称为方程式二。
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He chose the line so that--this is Gauss-- he chose the line to minimize the sum of squared distances of the points from the lines.
高斯选的这条线,所有点距离这条直线的平方和,是所有直线中最小的
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b It's RT over molar volume minus b minus a over molar volume V squared.
它等于RT除以摩尔体积V杠减去,再减去a除以摩尔体积的V杠平方。
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Thank you. Sorry, I've got the wrong glasses on but you're absolutely right, and in case the rest of you didn't hear it, n squared.
我看不清，但你绝对是对的,你们其他人可能没听清,是n的平方。
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d2G/dpdT So d squared G dT dp is equal to d squared G dp dT.
所以d2G/dTdp等于。
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Ever since this was first proposed, there has never been any observations that do not coincide with the idea, that did not match the fact that the probability density is equal to the wave function squared.
从未有，任何观测，与它相抵触,从没有过，波函数的平方不等于,概率密度的情况，关于马克思，波恩。
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So this squared at the origin is going to be a very high probability, and it decays off as you get farther and farther away from the nucleus or from the center, and that's independent of the angle.
所以这个平方,在原点处非常高，随着离核子的距离,越来越远,它逐渐衰减，并且它和角度是没有关系的。
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But luckily we don't have to worry about how we're going to picture all this, now that I said that, no physical interpretation f or a wave function, there is a physical interpretation for what a wave function squared means.
如何想象这些图像,我这么说，虽然波函数，物理解释,但波函数的平方，有物理解释,当我们说到。
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A joule is a kilogram meter squared per second squared.
一个焦耳等于,一千克乘以米的平方除以秒的平方。
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So instead of being equal to negative z squared, now we're equal to negative z effective squared times r h all over n squared.
这里不再等于-z的平方，现在我们等于-有效的z的平方,乘以RH除以n的平方。
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/2mv^2 We know that we have one-half mv squared.
我们现在已经有了一个。
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/2mv^2 So it is simply one-half mv squared.
它只是。
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