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Calculate $\ell=1$ eigenvalues and eigenvectors to the lowest non vanishing order in perturbation theory taking $$ H_0= \vec{L}^2 + \gamma L_z$$ as the unperturbed Hamiltonian and $$ H^\prime = \epsilon (L_xL_y+L_y L_x) $$ as perturbation.
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4727:Diamond Point
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