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I am confused that in general case, if [H,p]=0 (where H is Hamiltonian of system and P is parity operator), system wave function is either symmetric or antisymmetric. How do we know that system is in lower energy state if its wave function is symmetric by comparing that system is described by antisymmetric wave function? What I said is true or not? If true, what is physical significance behind?

thanks

xf

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# Why does the system has lower energy if its wave function is symmetric?

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