Pseudo-hermisyen teorinin sürekli reel spektrumu olan PT-simetrik delta fonksiyonlu potansiyele uygulanmasi

PT-symmetric Hamiltonians and their relation with pseudo-Hermiticity are introduced. For a diagonalizable Hamiltonian H with a discrete spectrum, equiv- alence of the reality of its spectrum and its E-pseudo-Hermiticity for some positive de¯nite operator E is shown. For such an E-pseudo-Hermitian Hamiltonian H de- ¯ned on a Hilbert space HS, physical Hilbert space HS(phys) which is consistent with Quantum Measurement Theory is constructed and its unitary equivalence with HS is shown. Then using pseudo-Hermitian Theory the Hamiltonian H, de¯ned on real line and having a PT-symmetric double Delta function potential with a purely imaginary coupling constant Z, is explored. The existence of a critical Z value Zc which ensures the reality of the spectrum for those Z values whose absolute value is less than the absolute value of Zc is shown. A biorthonormal system consisting of bounded eigen- function solutions of H and its adjoint is then chosen to construct a metric operator E up to the ¯rst order terms in Z. The equivalent Hermitian Hamiltonian h up to the second order terms in Z is then found. The result is used to calculate the energy ex- pectation values of some Gaussian wave packets and to examine the non-Hermiticity e®ect on those expectation values. Both in position and momentum spaces interaction regions, outside of which non-Hermiticity e®ect diminishes rapidly, are found.