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I am a second year physicist and I have completed 2 courses on quantum mechanics. The first was a decent overview of wave mechanics and the second was only 12 lectures long and applied this knowledge to the hydrogen and helium atoms and introduced aspects of atomic and molecular physics.

In the first course we were shown where the m and l quantum numbers came from when we began doing Quantum Mechanics in more than one dimension, however, in the second course we were told that the l quantum number is restricted to values between zero and n-1.

I have attached our lecture notes of the first course. In the first attachment (lecture 21) we introduce m on page 4. In the second attachment (lecture 24) we introduce l and show how m is restricted by it (see page 3) as a result of trying to find the functional form of the eigenvalues of angular momentum by using ladder operators however nowhere in the course were we shown the restriction on l by n.

Could someone please show me how this restriction arises?

Thanks a lot for any help.

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# Why does the l quantum number depend on n?

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