I am reading a quantum mechanics book. I did not clearly understand one particular idea.(adsbygoogle = window.adsbygoogle || []).push({});

When the book talks about the time-evolution operator [itex]U(t,t_0)[/itex], it says that one very important property is the unitary requirement for [itex]U(t,t_0)[/itex] that follows from probability conservation.

My question is, provided that the time-evoluation operator [itex]U(t,t_0)[/itex] satisfies the unitary requirement, that is, [itex]U(t,t_0)^{\dagger}U(t,t_0)=\mathbb{1}[/itex], how can I see and then proof explicitly that it indeed follows from probability conservation, that is, [itex]\sum_{a'}\left|c_{a'}(t_0)\right|^2=\sum_{a'}\left|c_{a'}(t)\right|^2[/itex]?

Thanks in advance for giving me a helping hand.

Reference: P.67, Modern Quantum Mechanics by Sakurai.

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# Unitarity of Time-evolution Operator

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