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## Homework Statement

Let the operator G={|ψ

_{1}>,|ψ

_{2}>,|ψ

_{3}>}, be orthonormal base in the Hilbert space. Now we make another operator U where U|ψ

_{i}>=|ψ

_{i+1}> for i=1,2 and U|ψ

_{3}>=|ψ

_{1}>. 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?