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Simultaneous eigenstate of angular momentum and hamiltonian
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[QUOTE="blue_leaf77, post: 5756529, member: 536596"] ##\Pi_1## is the parity operator in ##x## direction. It is defined by its action in position space on a wavefunction ##\psi(x_1,x_2,x_3)## by ##\Pi_1 \psi(x_1,x_2,x_3) = \psi(-x_1,x_2,x_3)##. But this is not necessary in the present problem since you are already given by its transformation properties. By expanding ##L_3 = x_1 p_2 - x_2 p_1## and using the properties of ##\Pi_1## as given in the question, calculate ##L_3 \Pi_1##. Don't compare them, one is the product between operators and the other one is the application of an operator on a state. No, it doesn't. It acts on the azimuthal coordinate instead, please review again your QM notes. [/QUOTE]
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Simultaneous eigenstate of angular momentum and hamiltonian
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