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Can a complex potential have real energies?

  1. Dec 4, 2005 #1
    Let be the Hamiltonian:

    [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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  3. Dec 4, 2005 #2

    ZapperZ

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