Prove that if a periodic Hamiltonian operator commutes with the translation operator then these two operators can have simultaneous eigenstates.(adsbygoogle = window.adsbygoogle || []).push({});

{{ H(x) = H(x+a) }

& { T(a)f(x) = f(x+a) }

& { [T(a),H(x)] = 0 }

}

--> {{[uni][psi] [subset] complex functions,there exists[psi] [subset] complex functions

such that{ H(x)[psi](x) = E[psi](x) }

& { T(a)[psi](x) = c(a)[psi](x) }

}

Thanks dudes.

eNtRopY

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# Commuation Relation

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