Abstract
We have studied a PT-symmetric quantum system for a class of position-dependent effective mass. Formalisms of supersymmetric quantum mechanics are utilized to construct the partner potentials. Since the system under consideration is not self-adjoint, the intertwining operators do not factorize the Hamiltonian. We have factorized the Hamiltonian with the aid of generalized annihilation and creation operators, which acts on a deformed coordinate and momentum space. The coherent state structure for the system is constructed from the eigenstates of the generalized annihilation operator. \\ It turns out that the self-adjoint deformed position and momentum operators violate the Heisenberg uncertainty principle for the PT-symmetric system. This violation depends solely on the PT-symmetric term, not on the choice of the inner product. For explicit construction, we have demonstrated, for simplicity, a constant mass PT-symmetric system Harmonic oscillator, which shows the violation of the uncertainty principle for a choice of acceptable parameter values. The result indicates that either PT-symmetric systems are a trivial extension of usual quantum mechanics or only suitable for open quantum systems.