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ArnarVidars
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Homework Statement
Let the operator G={|ψ1>,|ψ2>,|ψ3>}, be orthonormal base in the Hilbert space. Now we make another operator U where U|ψi>=|ψi+1> for i=1,2 and U|ψ3>=|ψ1>. Show that the operator U is unitary operator.
2. The attempt at a solution
I'm trying to argue that if the G operator is orthonormal base and there for unitary operator then U will also be an orthonormal operator and there for also unitary operator.
Since U is made from components that are orthogonal and they span the whole space then U is orthonormal and therefor unitary. Am I wrong?