So there is a theorem at the beginning of section 1.5 in Sakurai that states the following:(adsbygoogle = window.adsbygoogle || []).push({});

Given two sets of base kets, both satisfying orthonormality and completeness. there exists a unitary operator [itex]U[/itex] such that

[itex]|b^{(1)}> = U|a^{(1)}>,|b^{(2)}> = U|a^{(2)}>,...,|b^{(n)}> = U|a^{(n)}> [/itex]

By a unitary operator we mean an operator fulfilling the conditions

[itex]U^{t}U=1[/itex]

as well as

[itex]UU^{t}=1[/itex]

So this is not difficult to prove. But my real question is can we prove that [itex]U[/itex] is unique or is that just not the case and why?

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# Is the unitary operator unique?

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