At some point, your quantum physics instructor may ask you to find the eigenfunctions of Lz in spherical coordinates. In spherical coordinates, the Lz operator looks like this:

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which is the following:

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And because

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this equation can be written in this version:

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Cancelling out terms from the two sides of this equation gives you this differential equation:

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This looks easy to solve, and the solution is just

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where C is a constant of integration.

You can determine C by insisting that

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be normalized — that is, that the following hold true:

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(Remember that the asterisk symbol [*] means the complex conjugate. A complex conjugate flips the sign connecting the real and imaginary parts of a complex number.)

So this gives you

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You are now able to determine the form of

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which equals

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