I Why is the total number of quantum states = 2n^2 for some n?

[jerronimo3000]

If the number of possible values of L is n, and the number of possible values of m is 2*L-1, and there are 2 spin directions.. shouldn't the total number of states be 2*(number of possible L)*(Number of possible m)? But this gives 4n^2 - 2n. I am extremely confused. Thanks for your help!

 

[jtbell]

Each (different) value of l has a different number of possible of values of m, so you can't simply multiply (number of possible l)*(number of possible m).

 

[bahamagreen]

Looks to me like the values of l range from 0 to n-1 so no l value equals n.
The number of possible values of l is n, but the values of l don't equal n.

 

[jerronimo3000]

Each (different) value of l has a different number of possible of values of m, so you can't simply multiply (number of possible l)*(number of possible m).

Oh, duh..thanks, definitely clears that up! Thank you!