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And this spin magnetic quantum number we abbreviate as m sub s, so that's to differentiate from m sub l.
这个自旋磁量子数我们把它简写成ｍ下标ｓ,以和ｍ小标ｌ有所区分。
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In contrast, if we're taking the wave function and describing it in terms of n, l, m sub l, and now also, the spin, what are we describing here?
相反，如果我们考虑一个波函数,然后用ｎ，ｌ，ｍ小标ｌ,还有自旋，我们描述的是什么？
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Now I'll print L 2. Kind of what you'd guess, but here's the interesting question: if I say L 1 is assigned 0, L 1 sub is assigned 4, I'll print L 1.
然后我将显示下L2的内容，你，们猜猜这个有趣的问题：,如果我将L1赋值为4的话，再去显示下L1，会怎么样呢？
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No, we can't. Because if l equals 1, we can not have m sub l equal negative 2, right, because the magnetic quantum number only goes from negative l to positive l here.
不行，因为如果ｌ等于１,ｍｌ的值不可能等于－２，对吧，因为磁量子数的值,这时只能从－１到１
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PROFESSOR: OK. We can have n 4, l 3, and then, sure, we can have m sub l equal negative 2 if l equals 3 What's the second value of l that we can have?
教授：嗯，我们有ｎ４，ｌ３,然后我们有ｍｌ等于－２，如果ｌ等于３,ｌ可以有的第二个值是多少？
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So let's just think exactly what this means, and that means that if we take away function and we define it in terms of n, l and m sub l, what we're defining here is the complete description of an orbital.
让我们来考虑一下这是什么意思，这是说如果我们不考虑波函数,而是用ｎ，ｌ，ｍ下标ｌ来定义它，我们定义的,是一个轨道的完整描述。
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So, if we think of just an example, 2 we could say that 4 l equals 2, what would be our lowest value of m sub l?
举个例子，如果我们说l等于，那m小标l，最小值是多少？
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So the allowed values for m sub l 0 are going to be negative l, all the way up to 0, l and then up to positive l.
所以m小标l的可能值,是从负l，一直到，然后到正。
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ml=-2 So let's say we have n equals 4, and n sub l equalling negative 2.
这里n等于。
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m And the third one is called m, l it's also m sub l.
第三个量子数叫做，也叫做m小标。
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So when we talk about p orbitals, it's similar to talking about s orbitals, and the difference lies, and now we have a different value for l, so l equals 1 for a p orbital, and we know if we have l equal 1, we can have three different total orbitals that have sub-shell of l equalling 1.
当我们考虑ｐ轨道时，这和ｓ轨道的情形和相似，不同之处在于ｌ的值不一样，对于ｐ轨道，ｌ等于１,我们知道如果ｌ等于１,我们有３个,不同的轨道。
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The other main difference that we're really going to get to today is that in multi-electron atoms, orbital energies depend not just on the shell, which is what we saw before, not just on the value of n, but also on the angular momentum quantum l number. So they also depend on the sub-shell or l.
我们今天要讨论的,另一个很重要的区别就是,在多电子原子中，轨道能力不仅仅依赖于，我们以前看到的外层，不仅仅依赖于n的值，而是与角动量量子数也有关系,所以它们也依赖于亚外层或者。
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Yup. So m sub l could equal 2 negative 2, negative 1, 0, 1 or 2.
嗯，m下标l可以等于,2，-1，0，1，或。
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So we could have five values of m sub l.
所以它可以取5个值。
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So it's OK to not specify. I want to point out, pz whether you're in the p x, the p y, or the p z, unless a question specifically m asks you to specify the m sub l, which occasionally will happen, but if it doesn't happen you just write it like this.
我想指出的是，无论你在px，py或，除非一个问题特别地,让你指出l下面的，这种情况有时会发生，这样就可以了,但是如果它不做要求你们写成。
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n l So negative e, which is sub n l, because it's a function of n and l in terms of quantum numbers.
也就是负的，E，下标是，因为它是一个,关于量子数，n，和，l，的函数。
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