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We can graph out what this is where we're graphing the radial probability density as a function of the radius.
我们可以，画出它来,这是径向概率密度,作为半径的一个函数图。
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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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Identify the best responses of each player as a function of the others and find out where they intersect.
把每个人的最佳对策看成别人策略的函数,然后找出函数的交点
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It turns out there's a new function strlen S-T-R-L-E-N that you probably have not used yet called strlen, S-T-R-L-E-N, programmers early on and still like to be succinct but communicates sufficiently what they mean.
结果这里有个新的函数,你可能没有使用过，叫做，早期的和现在的程序员喜欢简洁地,但是能充分的传达他们的意思。
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same point Cartesian to have 1 representation for a point that supports different ways of getting information out, but has gathered within it, a method or a function for dealing with things like how do I know if it's the same point or not.
还有,这是一个比较极坐标的点,是否相同的不同的方法，但是这开始成了一个麻烦事儿了，我真正想要做的事情是,创建一个能支持不同的方式,输出已经收集的信息的点的表示。
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What we're talking about is literariness--that is to say, certain devices that we can identify that perform a certain function -and maybe out of the identification of these devices, to evolve a theory that's more widespread.
我们谈的是文学性，是一种我们能够认知并运用来达到一定目的的策略,我们需要进一步发展这个策略，使这个理论进化并传播。
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So we'd really like to be able to find some sort of equation of state, or some sort of rather function of state that's going to relate the heat going in or out of the system with that function of state, because this isn't going to do it.
所以我们真的想要去,找到一些态方程或者态函数,通过这个态函数可以表示热量,在系统与外界的交换,因为这个不能表示它。
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And it's important innovation in several different ways and we're going to talk about this whole science of building artificial organs, devices that are made out of totally synthetic components to replace the function of your natural organs, and the artificial heart is a good example of that.
在很多方向上也做出了重要的创新,我们会讲到,制造人造器官的技术原理,这些装置完全用合成材料制成,能够取代人体器官的功能,人造心脏就是一个很好的范例
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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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And again, I want to point out that a molecular orbital, we can also call that a wave function, they're the same thing.
同样，我要指出的是,一个分子轨道，我们也可以叫它波函数，这是一件事情。
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And, in fact, it kind of looks like a function, and yet here's a semicolon I just said that can get you into trouble, and yet that's not actually a function, because there's no interesting lines of code, because it turns out the interesting code is down here at the bottom.
实际上，它有点像一个函数，并且这里有一个能够使你陷入麻烦当中的分号,那个事实上也不是一个函数，因为这里没有有用的代码，因为,有用的代码都在底端。
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I'm not wasting time typing out arguments and implementing more complicated function.
我不会在浪费时间在打印输出参数上,我执行了更复杂的程序。
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So it turns out that, main, yes, is the default function you write, at least in C, when writing a program.
结果是，main函数，是的，这是你写的默认函数，至少是在C语言中，当写程序的时候。
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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 I want to figure out the best response of Firm 1 as a function of the price chosen by Firm 2.
我想找出公司1的最佳对策,并用公司2价格的函数表示
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So, it turns out that n is not the only quantum number needed to describe a wave function, however. There's two more you can see come out of it.
事实上，n不是描述一个波函数需要的,唯一的量子数，你们可以看到，还需要，两个量子数。
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Therefore, from experiments, u is only a function of temperature for an ideal gas, H and therefore from these experiments, 0 we come out with delta H dH/dp is equal to zero.
因此，从实验可以得出,对于理想气体u只是温度的态函数，因此从这些实验中我们得到Δ,偏H偏p等于。
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So we have the operationon the wave function in terms of r, theta, and phi and remember this e is just our binding energy for the electron, and we get back out this wave function.
我们用r，θ，φ来表示,将算符作用于波函数,而且记住e仅仅是电子结合能，然后后面加上波函数。
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We have Player I's payoff as a function of the two efforts and now I want to find out what is Player I's best efforts given a particular choice of S2? Yeah.
参与人I的收益是两人付出的函数,那么对于某个给定的S2,怎么计算参与人I的最佳对策呢
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Again we can look at this in terms of thinking about a picture this way, in terms of drawing the wave function out on an axis.
同样我们可以,用这个图像来考虑，从画轴上的波函数来考虑。
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It turns out there's actually no natural function known in the body for lithium.
事实上我们已知的身体机能,在正常情况下根本不需要锂。
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It means anybody using that little function get float doesn't have to worry about what's inside of it. So for example, I decide I want to change the message I print out, I don't have to change the function, I just pass in a different parameter.
这代表着用这个方法去获得浮点数,的任何人都不用担心具体的实现了,例如，如果我想改变下,显示的信息的话，我不必去改变方法，我传个不同的参数就可以了。
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You try to design actually I'm going to come back to that in a second. It's like you're trying to use a hash function that spread things out pretty evenly. But the places you store into in those lists may have to themselves have a small list in there, and when you go to check something, you may have to do a linear search through the elements in that list.
你尝试着去设计,实际上过会儿我会回头讲解这个问题,类似于你需要用一个哈希函数,非常平均的将物体分发出去,但是在列表中你数据,映射到的地方可能会有自己的一小段列表，当你回头查找数据的时候,你可能需要在那一小段列表中做线性查找。
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One of the things we said last time was, with that set of things, the ability to give values-- sorry, to give names to values-- the ability to make decisions, the ability to loop as a function of that, the ability get things in and out, we said that that actually gave us a language we said was Turing-complete.
上次我们和以上内容一起说过，我们可以赋值--抱歉,为数值命名--可以做出判断决定-,并且据此进行循环,可以输入输出数据,我们说拥有这些功能的语言,是图灵完备的。
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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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pxa So what happens when we add a 2 p a and we subtract from it a 2 p x b, or the same with a 2 p y a subtracting a 2 p y b, is that we're actually going to cancel out the wave function in the center, so we now have 2 nodal planes.
当我们用,减去2pxb时，或者是2pya减去2pyb时，我们会消去,中间的波函数，所以现在我们有两个节面。
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