- #1

Sekonda

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Hey,

This question is on determining the energies of a two particle system given the Hamiltonian, I believe it to be simple enough but would like you guys to check it and fill in any gaps in my reasoning

So I believe the eigenvalues of J^2 and J^2(z) are given by:

[tex]\hat{J}^{2}:j(j+1)\: ,\: \hat{J}^{2}_{z}:m(m+1)\Leftrightarrow \hbar=1[/tex]

('z' subscript same as '3')

and so the energy of state 1,1 is :

[tex]2(\alpha+\beta)[/tex]

The second part state that j=3, therefore m=3,2,1,0,-1,-2,-3

and so we just pop these into our eigenvalue equations above to attain the energies :

[tex]|3,3> : 12\alpha+12\beta\: ,\: |3,2>:12\alpha+6\beta[/tex]

etc.

Is this right?

Thanks for any comment/help!

SK

This question is on determining the energies of a two particle system given the Hamiltonian, I believe it to be simple enough but would like you guys to check it and fill in any gaps in my reasoning

So I believe the eigenvalues of J^2 and J^2(z) are given by:

[tex]\hat{J}^{2}:j(j+1)\: ,\: \hat{J}^{2}_{z}:m(m+1)\Leftrightarrow \hbar=1[/tex]

('z' subscript same as '3')

and so the energy of state 1,1 is :

[tex]2(\alpha+\beta)[/tex]

The second part state that j=3, therefore m=3,2,1,0,-1,-2,-3

and so we just pop these into our eigenvalue equations above to attain the energies :

[tex]|3,3> : 12\alpha+12\beta\: ,\: |3,2>:12\alpha+6\beta[/tex]

etc.

Is this right?

Thanks for any comment/help!

SK

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