Can a complex potential have real roots?

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Let be the Quantum Potential V(x)=A(x)+iB(x) with A and B real functions then my question is if this potential will have real roots if we take the expected value:

[tex]E_{n}=<\phi|H|\phi> [/tex] then the complex part of the energies will come from the expected value <B> so for real energies B should be Zero,but using Ehrenfrest,s theorem:

[tex]i\hbar\frac{d<B>}{dt}=<[B,H]>[/tex] B and H should commute, but we have that x and p do not commute so <B> can not be zero and there won,t be any real roots...

sorry: with "roots" i meant energies....
 
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