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

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SUMMARY

The azimuthal quantum number, denoted as 'm', plays a crucial role in quantum mechanics by defining the angular momentum states of a quantum system. In the context of spin-1 particles, 'm' values of +1 and -1 represent states that change appearance upon rotation, while 'm=0' remains unchanged during a full rotation of 2π. This behavior illustrates the distinction between classical and quantum systems, where 'm=+1' and 'm=-1' correspond to classical spinning objects, and 'm=0' relates to oscillating motion along an axis.

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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!
 
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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.
 
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