- #1

eNtRopY

Prove that if a periodic Hamiltonian operator commutes with the translation operator then these two operators can have simultaneous eigenstates.

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

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

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

}

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

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

}

Thanks dudes.

eNtRopY

{{ 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

Last edited by a moderator: