1. Nov 28, 2004

### rgshankar76

What is the physical significance of the various quantum numbers like (l,m,s,j, etc)that are used to describe any system.

2. Nov 28, 2004

### RedX

Well l is usually orbital angular momentum, m is orbital angular momentum along an axis, s is spin, and j is total angular momentum.

Actually l is a number which represents orbital angular momentum. The real value would be sqrt [l(l+1)h^2] I think, where h is planck's constant divided by 2pi. Upon further consideration, yeah, you have m going from -l to l. Similarly for spin and total angular momentum.

Anyways, physically these quantum numbers will tell you what you will observe if you make a measurement of something you can observe. If a value of some observable is not one of these quantum numbers, then you won't observe it. For example if you take a particle where s=1/2, then if you measure the spin, then you'll get sqrt(1/2(1/2+1)h^2) because that's the only allowed value when you specify s=1/2.

Also all these quantum numbers may not have definite values simultaneously. You'll have to consider whether all the operators commute or not and can be simultaneously diagnoalized by a unitary change of basis. Some things always commute like the total angular momentum operator and one of the total angular momentum operators about an axis. Others don't like the total angular momentum operators about an axis with each other.