Abstract
We investigate the possibility of existence of dynamical invariant(s) for a few complex (non-hermitian) Hamiltonian systems H(x, p), in one dimension. For this purpose, we consider an extended complex phase space, characterized by x = x1 + ip2, p = p1 + ix2. We make use of the much discussed rationalization method to construct the invariants for a class of complex polynomial potentials that also includes some PT-symmetric ones.
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