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[QUE/QM-23004]

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A particle moves in two dimensional circular oscillator potential $$  V(x) = {1\over 2} m \omega^2(x^2+y^2) $$ (a) What are the quantum numbers of the first excited state? Is it degenerate or not?
(b) If a small perturbation $H^\prime =  \lambda xy $ is applied compute the lowest order correction to the energy of the first excited state.     

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