# Continuity Equation in Quantum Mechanics when potential is a complex valued function

How can we derive the continuity equation from Schrodinger equation if the potential is a complex function of position? What I tried was the general $$1-D$$ derivation of the Continuity equation from Schrodinger equation and got the result: $$\frac{\partial \rho}{\partial t} = -\frac{\partial j}{\partial x} + \frac{\rho(x,t)}{i\hbar}\left[V(x) - V^*(x)\right]$$ where, $$j$$ is the probability current density. My doubt is what physics does the term $$\frac{\rho(x,t)}{i\hbar}\left[V(x) - V^*(x)\right]$$ convey?

• Note that $V(x) - V^{*}(x) = 2i \Im(V(x))$
– nox
Nov 9, 2021 at 23:11