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qB This must be heat q B, right. So again, but now let's also look at our special function.
这个不是，这应该是热量，对吧？所以又一次，这些是我们熟悉的。
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This is the name to which I'm going to refer when I want to use this function. All right?
这是我以后使用这个函数式,会采用的名字？
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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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So again, for both heat and work we don't get the same result. Now let's look at our special function, right. So here's path A.
所以，再一次说明，对于热量和功,我们得到的结果是不同的,现在让我们看看我们的特殊函数。
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Because certainly there is a theory that art's main function is to provide succor and solace in this "vail of tears". -Right.
因为确实有一种理论认为艺术的主要,功能是提供帮助与安慰,因为世界纷繁而痛苦，-对的。
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So this line represents the expected payoff of shooting to the middle as a function of the probability that the goal keeper dives to the right.
这条线表示从中路射门时罚球者的收益,是门将扑向右路概率的一个函数
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All right,so this is something that's-- If the personality function's been destroyed, can't be recovered,can't be fixed, but the rest of the bodily functioning is still going on.
如果有这样的例子-,人格功能被破坏，无法修复，但剩下的生理功能仍在继续。
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This function will have the right second derivative.
这个函数会得出正确的二阶导数
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Of course, we will also be talking about behavioral finance in this course and we'll, at times, be saying that the utility function concept isn't always right-- the idea that people are actually maximizing expected utility might not be entirely accurate.
当然 我们还会,在这门课上讨论行为金融学,并且,我们会间或,讨论到效用函数不总是正确的,人们希望最大化期望效用的观点,也许并不是完全准确的
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In function, main. All right.
在main函数中，好的。
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If you run these curves only on non-smokers you get rid of that J at the end of the curve and you get pretty much a function that's to the right of the curve here.
如果仅在不吸烟人群中做统计,那么左末端就不会出现J形曲线,而是会得到一条,从左到右逐渐上升的完美的函数曲线
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How many steps does it take for this function to run? Well, you can kind of look at it, right?
这个方法运行了多少补？,你可以看看代码？
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But right now, what I want you to be thinking of a wave function as is just some representation of an electron.
但是现在，我想让你们,将波函数仅仅理解为,一个电子的表示方法。
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This is me writing one hour of that episode of Pirandello and telling the other authors, here's what I'm assuming as you use it. So it's up to me to do it right, but if I do it, I'm going to specify, what does this function do?
作为一个程序员,我得为用户提供一些信息,这正是我写写的皮兰德娄戏剧的一小时片段,并且要告诉其它的作家，这是我希望你使用的地方，所以由我决定怎样去做好它？
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It's a state function. If we know the enthalpy of the products minus the enthalpy of the reactants, right. It's a state function.
如果我们知道生成物的焓减,去反应物的焓的值,它是个态函数，原则上我们可以做到。
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This is another way of doing exponentiation, but this one's a recursive function. All right?
但这是一种递归的方法对不对？,好，让我们看看这种方法？
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And here's my green line representing my expected payoff as the shooter, from shooting to the right, as a function of the probability that the goalie dives to the right.
这条绿线表示作为一个罚球球员,我从右路射门的收益,是门将扑向右路概率的一个函数
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All right. So hopefully we're pretty comfortable naming any type of wave function using the chemist terminology.
好了，希望我们都可以,接受这种,用化学术语来命名任何类型的波函数了。
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All right? So I've created this function let's give it a shot and see what happens.
好，大家看到我已经创建这个函数了,让我们试试看怎么样。
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So, what this means is that when we're looking at an actual wave function, we're treating it as a wave, right, so waves can have both magnitude, but they can also have a direction, so they can be either positive or negative.
这意味着,当我们看一个波函数时,我们把它看做一个波，波不仅有幅值，还有方向，所以它们可正可负，如果。
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This is the payoff to Player I of choosing Middle against Right, and the line in between, this line here, is the expected payoff to Player I of choosing Middle as a function of the probability that other people choose Right.
这条表示对手选右时参与人选中的收益,两个端点中间的线段部分,表示参与人I选右的预期收益,它是对手选右概率的一个方程
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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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