(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the unitary time evolution time operator requires that the Hamiltonian

be hermitian.

And then it tells us to use the infinitesimal time evolution operator.

3. The attempt at a solution

[itex] U(dt)=1-\frac{iHdt}{\hbar} [/itex]

so now we take [itex] U^tU=(1+\frac{iH^tdt}{\hbar})( 1-\frac{iHdt}{\hbar}) [/itex]

When I multiply this out it still is not obvious to me why H need to be hermitian.

although I could make an argument about the cross terms with i's in them

if H is not hermitian then I would have an imaginary number in my expansion and that would

not be equal to 1. But then my last term with H^tH might have some i's in it to cancel the i's from the cross terms but if this were the case H would need to have i's in it and the cross terms would not have i's after they were multiplied to H.

What do you guys think.

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# Homework Help: Show that H is hermitian.

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