# I Quantum numbers - Total Energy and Orbital Momentum

1. Apr 23, 2016

### klw289

With the quantum numbers l=1, n=2 and m=-1 how do I calculate the total energy E, L2 (the square of the orbital momentum) and Lz (the z-component of the orbital angular momentum.

2. Apr 23, 2016

### stevendaryl

Staff Emeritus
Is this a homework problem? If so, it should be moved to the homework section, and should be put in the proper homework problem format.

3. Apr 23, 2016

### klw289

This was not "homework" I am just reading a physics book for my own enjoyment and I was reading a section and I have no clue how to get started. I could post it in homework if its more suitable?

4. Apr 23, 2016

### stevendaryl

Staff Emeritus
Well, the actual way that these things are figured out is to start with Schrodinger's equation. That's a pretty complicated undertaking, which can't really be described in a post. If you just want to skip to the answers: For a hydrogen atom,

$E = \frac{- m q^4}{\hbar^2 n^2}$

where $m$ is the mass of an electron, $q$ is the charge of an electron (in CSU units), $n$ is the principal quantum number, and $\hbar$ is Planck's constant.

$L = \sqrt{l(l+1)} \hbar$
$L_z = m \hbar$

For an atom other than a hydrogen atom, replace $q^4$ by $N^2q^4$, where $N$ is the number of protons in the atom.

5. Apr 23, 2016

### Staff: Mentor

We consider this to be a "homework-like" problem. If your trouble is that you can't find the appropriate formulas, try here:

http://hyperphysics.phy-astr.gsu.edu/hbase/qunoh.html

If you have the formulas but you can't get the numbers to come out right, go to the Introductory Physics Homework forum:

https://www.physicsforums.com/forums/introductory-physics-homework.153/

Post what you've done (show your work), and someone can probably find your mistake.

(stevendaryl slipped in ahead of me)

6. Apr 23, 2016

### klw289

Thank you, that can get me started. I'll also go back to schrodingers equation.