Quantum mechanics , total orbital angular momentum?

[Outrageous]

Homework Statement

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?

Homework Equations

n>l, l is bigger or equal to m

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?
Please guide ,thanks

 

[vela]

Homework Statement

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?

Homework Equations

n>l, l is bigger or equal to m

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?
Please guide ,thanks

Read your textbook and notes and answer the following questions:

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 $L_z$?

 

[Outrageous]

Read your textbook and notes and answer the following questions:

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 $L_z$?

$\vec{L}^2$ 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)

 

[vela]

$\vec{L}^2$ mean the angular momentum square
$L_z$ angular momentum in z direction
$\vec{L}^2=l(l+1)\hbar$ and $L_z=m\hbar$.

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.

Total orbit angular momentum is j?
J=l-(1/2) or l+(1/2)

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