Date of Award


Degree Type


University or Center

Clark Atlanta University(CAU)


School of Arts and Sciences

Degree Name




First Advisor

Dr. Xiao-Qian Wang

Second Advisor

Dr. George Japaridze

Third Advisor

Dr. Swaraj S. Tayal


Bender and Boettcher explored a quantum theory based on a non-Hermitian PT­ symmetric Hamiltonian , where PT is the operator of the space-time reflection and demonstrated that the PT-symmetric Hamiltonian can possess entirely real spectra. In this thesis, we point out that in the framework of PT-symmetric quantum mechanics; the calculation of matrix elements in the Hilbert space is ill-defined. We point out the importance of using CPT inner product in PT-symmetric systems. We manifested our assessment using the CPT inner product prescription for the entangled wave function of the composite system. We show that for a composite system with a local PT-symmetry, it preserves the no-signaling condition and the orthogonality of the states.The reduced density matrix is diagonal and independent of the non-Hermitian parameter . We reaffirm the consistency of PT-symmetric quantum mechanics as a candidate for a fundamental theory .