In "The Theoretical Minimum" of Susskind (p.98) it says that if we take any two basisvectors [itex]|i \rangle[/itex] and [itex]|j \rangle[/itex] of any orthonormal basis, and we take any linear time-development operator [itex]U[/itex], that the inner product between [itex]U(t)|i \rangle[/itex] and [itex]U(t)|j \rangle[/itex] should be 1 if [itex]|i \rangle=|j \rangle[/itex]. Why is this so? (Why is the product normalized?) I can see how it is demonstrated that the inner product of [itex]U(t)|i \rangle[/itex] and [itex]U(t)|j \rangle[/itex] is 0 if [itex]|i \rangle \neq |j \rangle[/itex] (in fact, he assumes it). The reasoning is aimed to show that time evolution is unitary.(adsbygoogle = window.adsbygoogle || []).push({});

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# I Proof of unitarity of time evolution in Susskind's book

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