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## Homework Statement

(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.

## Homework Equations

[tex]

$ J=L+S $\\

$ j=l \pm s $\\

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

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

[/tex]

## 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?