What is the significance of azimuthal quantum numbers in quantum mechanics?

[livelife92]

this isn't a numerical problem...thought i hope its fine posting here...
i don't understand the concept of azimuthal/angular momentum quantum number..
please help.
i searched this site 4 aa very basic level explanation...also the web...couldnt find much.please help!

 

[turin]

First consider spin-1, which is like the QM version of "ordinary".

If you take a snapshot of the state and then rotate it, then m=+1 or -1 will look different as you rotate, and then return to the original state after a complete rotation of 2pi, and m=0 will look the same the whole way around.

If you simply observe the state as it oscillates, then any state, m=+1, -1, or 0, will change during the oscilation, and will return to the original state once per period.

m=+1 or -1 is analogous to a classical object spining around the axis, and m=0 is analogous to a classical object oscillating up and down along the axis at the given rotational frequency.