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You see, the quantum condition, by putting quantization into the moangular mentum it is propagated through the entire system. Orbit dimensions are quantized.
你们看，量子条件，通过把,角动量量子化，它就能在这个系统中进行传播,同时轨道大小也被量子化。
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Now, you recall in Bohr the quantum condition.
现在，回忆一下波尔量子理论。
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So, let's see how some of this works, and hopefully your counterparts from 100 years ago would also be able to think about how this works, even if they don't have the quantum mechanics behind the individual electron configurations for atoms.
那么，下面让我们来看一下它是怎么用的，希望一百年前想你们一样的同学,也能够弄懂它为什么能用，尽管他们没有量子力学,不知道原子的电子排布。
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We use the adjective "Newtonian" but we don't speak of certain writers who are still interested in quantum mechanics as "Newtonian writers."
虽然我们用牛顿主义者这个词“,但是我们不会把那些,对量子力学有兴趣的人称作牛顿主义作家“
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But the answer is, according to the standard interpretation of quantum mechanics, that's not how it works.
但答案是,根据量子力学的标准解释,这并非如此
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Bohr expressed the quantum condition by the angular momentum, quantum condition in the following manner.
波尔阐明了他的量子理条件,通过角动量，和以下的量子条件进行量子化。
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He did not invoke the quantum condition, but he gets to the quantum condition.
他不是求助于量子化条件，而是他得到了一个量子化条件。
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b The repulsive term goes as some constant lower case b divided by R to the n. N is not the quantum number.
这种斥力很想一个固定的小写字母,被R到n分开的话，N不是量子数。
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So, the quantum mechanical interpretation is that we can, in fact, have probability density here and probability density there, without having any probability of having the electron in the space between.
量子力学给出的解释是，实际上，我们可以在这有概率密度，在这里有概率密度,但在两个之间没有。
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And specifically, MO theory is the quantum mechanical description of wave functions within molecules.
特别的，MO理论是,分子内波函数的描述。
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Specify the quantum number n and divide by Z.
只需说明n的具体值，并用Z去除就行了。
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n So the velocity is given by this product of the quantum number n Planck constant 2 pi mass of the electron time the radius of the orbit, which itself is a function of n.
速度是量子数,普朗克常数2π乘以轨道半径的值,它自身也是n的函数。
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The other thing that we took note as is what happens as l increases, and specifically as l increases for any given the principle quantum number.
另外一个我们要注意的是,ｌ增加时如何变化，特别是对于某个给定的,主量子数ｌ变化时如何变化。
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And when you solved the relativistic form of the Schrodinger equation, what you end up with is that you can have two possible values for the magnetic spin quantum number.
当你们解相对论形式的,薛定谔方程，你们最后会得到两个,可能的自旋磁量子数的值。
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But the reality that we know from our quantum mechanical model, is that we can't know exactly what the radius is, all we can say is what the probability is of the radius being at certain different points.
我们不可能准确的知道,半径是多少，我们只能说，它在不同半径处，的概率是多少，这是,量子力学。
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The way he described is when you try to get down a quantum dimensions and you are standing there with your camera, just remember the sun is at your back and your shadow is always in the picture.
这种方法被他描述为,当你试着处理一个量子尺寸时,并且你试着拿着你的相机在那，记住太阳在你的背后,而你的影子总是在照片上。
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The reason there are three quantum numbers is we're describing an orbital in three dimensions, so it makes sense that we would need to describe in terms of three different quantum numbers.
我们需要，3个量子数的原因,是因为我们描述的是一个，三维的轨道，所以我们需要，3个不同的量子数,来描述它。
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So, we'll take a little bit of a step back after we introduce quantum mechanics, and talk about light as a wave, and the characteristic of waves, and then light as a particle. And one example of this is in the photoelectric effect.
等我们介绍完量子力学后,我们要回过头来讨论下光,作为一种波和它的波动性特征,以及光作为一种粒子,其中的一个粒子就是光电效应。
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This is the proportionality that is multiplied by the quantum.
这就是与量子的,比例系数。
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For an f orbital, what is the quantum number l equal to?
对于一个，f，轨道，它的角量子数，l，等于几？
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what three quantum numbers tell us, versus what the fourth quantum number can fill in for us in terms of information.
三个量子数和,四个量子数告诉我们的信息。
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So we can have, if we have the final quantum number m equal plus 1 or minus 1, we're dealing with a p x or a p y orbital.
所以如果我们有,磁量子数ｍ等于正负１,我们讨论的就是ｐｘ或者ｐｙ轨道。
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But at the time, they didn't have a well-formed name for it, they were just saying OK, there's this fourth quantum number, there's this intrinsic property in the electron.
但在那时，人们没有给它取名，他们只是说ｏｋ，这是第四个量子数，这是电子的本征性质，
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We can not do that with quantum mechanics, the more true picture is the best we can get to is talk about what the probability is of finding the electron at any given nucleus.
在量子力学里我们不这样做，我们能得到的更加真实的图像,是关于在某处,找到电子的概率。
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So now we're just counting up our orbitals, an orbital is completely described by the 3 quantum numbers.
所以现在我们只要把这些轨道加起来，一个轨道是由３个量子数完全确定的。
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1/2 And we have the spin quantum number 2 as plus 1/2 for electron one, -1/2 and minus 1/2 for the electron two.
我们有自旋量子数,对于电子，我们有自旋量子数。
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- The same place is that energy is a function of these four quantum numbers.
它就是这个结论,能量是这四个量子数的机能显示。
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I think this is taken about two years after they discovered the fourth quantum number.
这张照片拍摄于他们发现,第四个量子数的两年后。
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The fundamental laws of physics, according to the standard interpretation of quantum mechanics, are probabilistic.
物理学的基本法则,根据量子力学的标准解释来说,这都是概率决定的
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And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.
此外，当我们解波函数,或者考虑薛定谔方程的结果时，我们看到的确３个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。
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