# Quantum mechanics , total orbital angular momentum?

1. Jan 1, 2014

### Outrageous

1. The problem statement, all variables and given/known data

A hydrogen atom is identified as being in a state with n=4. What is the magnitude of the total orbital angular momentum for the largest permitted value of l?

2. Relevant equations
n>l, l is bigger or equal to m

3. The attempt at a solution
The allowed l= 3,2,1
The allowed m for largest l= 3,2,1,0,-1,-2,-3
Total orbital angular momentum is the sum of all Lz or L^2?
Ans, total= 3+2+1+0 +(-1)+(-2)+(-3)=0?
L^2= 3(3+1)hbar
What is the total orbital angular momentum?

2. Jan 1, 2014

### vela

Staff Emeritus
1. What does $\vec{L}^2$ physically represent?
2. What about $L_z$?
3. How are $l$ and $m$ related to $\vec{L}^2$ and $L_z$?

3. Jan 1, 2014

### Outrageous

$\vec{L}^2$ mean the angular momentum square
$L_z$ angular momentum in z direction
$\vec{L}^2$=l(l+1)\hbar and $L_z$=m\hbar.
Total orbit angular momentum is j?
J=l-(1/2) or l+(1/2)

4. Jan 1, 2014

### vela

Staff Emeritus
That should be $\vec{L}^2=l(l+1)\hbar^2$. Total orbital angular momentum means not just the z-component. $m$ and $l$ are quantum numbers, not angular momenta.

The key word here is orbital. Which observable corresponds to orbital angular momentum?