PT Symmetric Hamiltonian Model and Exactly Solvable Potentials

Yesiltas Ö.

1st International Conference on Mathematical Modelling in Physical Sciences (IC-MSQUARE), Budapest, Hungary, 3 - 07 September 2012, vol.410 identifier identifier


Searching for non-Hermitian, PT-symmetric Hamiltonians [I] with real spectra has been acquiring much interest for fourteen years. In this article, we have introduced a PT symmetric non-Hermitian Hamiltonian model which is given as (H) over cap = omega((b) over cap (dagger)(b) over cap + 1/2) + alpha((b) over cap (2) - ((b) over cap (dagger))(2)) where omega and alpha are real constants, (b) over cap and (b) over cap (dagger)are first order differential operators. Because the Hamiltonian H is pseudo-Hermitian, we have obtained the Hermitian equivalent of H which is in Sturm-Liouville form leads to exactly solvable potential models which are effective screened and hyperbolic Rosen-Morse II potentials. Using convenient sinilarity transformations, we have obtained a physical Hamiltonian h for each case. Then, the Schrodinger equation is solved exactly using Shape Invariance method of Supersymmetric Quantum Mechanics [2].