Complex integrals for 3-dimensional non-hermitian Hamiltonian systems

With a view to obtain further insight into the theoretical understanding of complex potentials, we here investigated the dynamical invariants for time-independent (TID) complex Hamiltonian systems in three dimensions by invoking the elegante extended complex phase space approach (ECPSA) characterized by x=x1+ip4,y=x2+ip5,z=x3+ip6,px=p1+ix4,py=p2+ix5 and pz=p3+ix6. We make use of rationalization method for this purpose and the invariants so obtained are expected to play an important role in studying the non-hermitian Hamiltonian systems.