(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(a) Consider a system composed of two electrons with orbital angular momentum

quantum numbers l_1 = 4 and l_2 = 2.

Give all the possible values of

(i) the total orbital angular momentum quantum number L,

(ii) the total angular momentum quantum number J. [8]

(b) Explain what is meant by the parity of an atomic or nuclear state. Show that

the state described by the wave-function [tex] $\psi= r cos \theta exp(r/2a) $ [/tex] has parity

quantum number -1.

2. Relevant equations

[tex]

$ J=L+S $\\

$ j=l \pm s $\\

$ L^2 = l(l+1) $\\

$ P \psi = e^{i\theta}\psi $

[/tex]

3. The attempt at a solution

I know this is probably extremely easy but I've been given no examples and I keep getting myself in a muddle. Are the answers for L and J suppose to come out as non integers?

[tex]

$ L^2 = l(l+1) $\\

$ L_1=\sqrt{20} = \pm 4.47 $ \\

$ L_2=\sqrt{6} = \pm 2.449 $\\

L = -6.919, -2.021, 2.021, 6.919

[/tex]

Are the negative values valid?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spin Orbit Interaction

**Physics Forums | Science Articles, Homework Help, Discussion**