Let be the Hamiltonian:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]H=T+V [/tex] where [tex]V(x)=A(x)+iB(x) [/tex]

then my question is if the Hamiltonian will have real energies..if we apply Ehrenfrest,s theorem for B:

[tex]i\hbar{\frac{d<B>}{dt}}=<[B,H]>[/tex]

then if B is a function of x and x and p do not commute the derivative of <B> can not be zero so its integral is also non-zero so we will always have that:

[tex]E=<H>=<T>+<A>+i<B> [/tex]

so the expected value of the Hamiltonian (the energy) will be complex.

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# Can a complex potential have real energies?

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