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But in return,Heller's surfing adventure helped him learn a valuable lesson about catching the perfect wave in life.
VOA: standard.2010.08.04
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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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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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And the thing about what Schrodinger did was all he imposed on a system was the electron behaves as a wave and is bound.
薛定谔所做的,是建立在一个系统之上,电子是像波一样运动的并且是有界限的。
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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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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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So you're basically having a wave equation for a particle, and for our purposes we're talking about a very particular particle. What we're interested in is the electron.
所以你们主要有,一个粒子的波动方程，我们的目的是考虑一个特殊的粒子,我们感兴趣的是电子。
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So, we're talking about wave functions and we know that means orbitals, but this is -- probably the better way to think about is the physical interpretation of the wave function.
我们讨论波函数而且,我们知道它代表着轨道，但-也许更好的思考方法是,考虑波函数的物理意义。
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We talked about the wave function for a 2 s orbital, and also for a 3 s orbital.
我们讲过２ｓ轨道的波函数，也讲过３ｓ轨道。
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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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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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But when we're thinking about actual wave behavior of electrons, it's just important to keep in the back of our head that some areas have positive amplitude and some have negative.
电子的波动行为时,我们，要记住,某些地方是正的,某些地方是负的,当我们讲到。
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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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We also talked about well, what is that when we say wave function, what does that actually mean?
我们还说了，当我们讨论波函数时，它到底有什么意义？
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So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。
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So, as an example, let's take argon, I've written up the electron configuration here, and let's think about what some of the similarities might be between wave functions in argon and wave functions for hydrogen.
所以作为一个例子我们来看看氩，我已经把它的电子构型写在这里，我们来考虑氩和,氢波函数之间的,一些相似性。
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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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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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But now we're talking not about an atomic wave function, we're talking about a molecular wave function.
但现在我们不是讨论原子的波函数，我们讨论的是分子的波函数。
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So, we can think about what is it that we would call the ground state wave function.
我们来考虑一下,基态的波函数，是怎么样的。
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So on Friday, we'll start with talking about the wave functions for the multi-electron atoms.
在周五，我们要开始讨论,多电子原子的波函数。
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And in doing that, we'll also talk about the shapes of h atom wave functions, specifically the shapes of orbitals, and then radial probability distribution, which will make sense when we get to it.
为了这样做，我们要讲一讲，氢原子，波函数的形状，特别是轨道的形状，然后要讲到径向概率分布，当我们讲到它时，你们更能理解。
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So, you remember from last time radial nodes are values of r at which the wave function and wave function squared are zero, so the difference is now we're just talking about the angular part of the wave function.
你们记得上次说径向节点在,波函数和波函数的平方,等于零的ｒ的处，现在的区别是我们讨论的是,角向波函数。
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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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Once we can do that we can go on and say okay, what actually is a wave function, but first we need to know how to describe which ones were talking about.
我们就可以继续并说波函数到底是什么,但首先，我们需要知道，如何描述,我们说的,是哪一个波函数。
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So now that we can do this, we can compare and think about, we know how to consider wave functions for individual electrons in multi-electron atoms using those Hartree orbitals or the one electron wave approximations.
现在我们可以做这些了，我们可以对比和考虑，我们知道如何用哈特里轨道,或者单电子波近似去考虑,多电子原子中的单个电子波函数,所以对于我们研究了。
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The reason that we can talk about this is remember that we're talking about wave functions, we're talking about waves, so we can have constructive interference in which two different orbitals can constructively interfere, we can also have destructive interference.
我们可以这么说的原因是,记住我们说的是波函数，我们说的是波函数，所以我们可以得到相长干涉,这是两个不同轨道会相长干涉，我们也有相消干涉。
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There's no classical way to think about what a wave function is.
我们没有办法从经典力学的角度,想象波函数是什么样的，没有经典的类比。
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