1. The problem statement, all variables and given/known data Given a non-hermitian hamiltonian with V = (Re)V -i(Im)V. By deriving the conservation of probability, it can be shown that the total probability of finding a system/particle decreases exponentially as e(-2*ImV*t)/ħ 2. Relevant equations Schrodinger Eqn, conservation of probability (∂P/∂t = -∇⋅j), P is the probability and j is the probability current density, Re V is the real part of V while Im V is the imaginary part of V 3. The attempt at a solution It is known that ∫∫∫ P d3r = constant, that is ,the total probability for finding the particle should be constant throughout the universe. iħ ∂ψ/∂t = -ħ2/2m ∇2ψ + Vψ = -ħ2/2m ∇2ψ + (Re)Vψ -i(Im)Vψ By taking the complex conjugate, we have -iħ ∂ψ*/∂t = -ħ2/2m ∇2ψ* +V*ψ* = -ħ2/2m ∇2ψ* + (Re)Vψ* +i(Im)Vψ* By multiplying by ψ* the first equation and by ψ the second equation then subtracting the second from the first, we have iħ ∂(ψψ*)/∂t = -ħ2/2m (ψ*∇2ψ-ψ∇2ψ*) - 2i (Im)V ψψ* = -∇⋅j - 2i (Im)V ψψ* I don't know where to go already from here. Any suggestions or hints?