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I'm having a difficult time understanding something.

On yet another attempt to deepen my quantum mechanics understanding I referred to the widely recommended book of Griffiths.

I find the book indeed very good and pretty thorough in it's scope. There is one thing however I was unable to get from the book.

Griffiths develops the quantum number "l" in two different ways: In the first way - the "ugly" way, "l"'s origin is being a separation variable (more accurately, l(l+1) ) between the radial and angular expressions retrieved from the spherical Hamiltonian while looking for separable solutions. In this development however he concludes that l has to be a whole integer because of the cyclic nature [itex]\phi[/itex] imposes. ([itex] e^{i\phi} = e^{i\phi + 2\pi})[/itex].

Later, he develops the angular momentum operators which carry their "l"'s as their eigenvalues, and with help of ladder operators shows eventually the equivalence of this l with the last l.

However, in this way, he concludes that l isn't nessecarily whole, and that also half-integers are allowed.

What he doesn't bother to explain, is how come we didn't get these values from the first technique? How come we get a condition that forces that l's to be whole? And how do the half integers not contradict the cyclic nature of [itex]\phi[/itex]?

Thanks a lot!

Tomer.

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# Half integer orbital momentum, following Griffiths

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