Probability of crossing S per wit tyne. The differential version of 19.41 = 0 - the continuity equation (19.5)2. Let us consider a Hamiltonian for a particle of mass m in which the potential energy is a complex function, specifically, h2 H = - -A+ U(r). U(r) = Uj(r) + iU,(r) (1) 2m where Un (r) are real functions. Show that the change of probability with time to find a particle within a volume / is no longer uniquely determined by the probability flux characterized by the vector in j = (pVy*- 4*VY) (2) 2m across the surface S enclosing the volume 1. To demonstrate, you need to re-derive the continuity equations for the probability density, both in the integral and differential forms, Eqs. (19.4) and (19.5) of the lecture notes. Violation of the continuity equation can be interpreted as an absorption or creation of particles in an external field. How is the sign of U,(r) tells us whether we are dealing with absorption or creation