Quantum Physics For Dummies, Revised Edition
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In quantum physics, you can find the eigenvalues of the raising and lowering angular momentum operators, which raise and lower a state’s z component of angular momentum.

Start by taking a look at L+, and plan to solve for c:

L+| l, m > = c | l, m + 1 >

So L+ | l, m > gives you a new state, and multiplying that new state by its transpose should give you c2:

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To see this equation, note that

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On the other hand, also note that

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so you have

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What do you do about L+ L? Well, you assume that the following is true:

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So your equation becomes the following:

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Great! That means that c is equal to

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So what is

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Applying the L2 and Lz operators gives you this value for c:

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And that’s the eigenvalue of L+, which means you have this relation:

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Similarly, you can show that L gives you the following:

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About This Article

This article is from the book:

About the book author:

Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). He graduated from MIT and did his PhD in physics at Cornell University, where he was on the teaching faculty for 10 years. He’s also been on the faculty of MIT. Steve also teaches corporate groups around the country.

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