# Can a complex potential have real energies?

1. Dec 4, 2005

### eljose

Let be the Hamiltonian:

$$H=T+V$$ where $$V(x)=A(x)+iB(x)$$

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

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

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:

$$E=<H>=<T>+<A>+i<B>$$

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

2. Dec 4, 2005

### ZapperZ

Staff Emeritus