- #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, 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
{{ 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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