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 *c*^{2}:

To see this equation, note that

On the other hand, also note that

so you have

What do you do about L_{+} L_{–}? Well, you assume that the following is true:

So your equation becomes the following:

Great! That means that *c* is equal to

So what is

Applying the L^{2} and L* _{z}* operators gives you this value for

*c*:

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

Similarly, you can show that L_{–} gives you the following: