$\mathcal {PT}$ symmetric Hamiltonian model and Dirac equation in 1+1 dimensions$\mathcal {PT}$ symmetric Hamiltonian model and Dirac equation in 1+1 dimensions

Özlem Yeşiltaş

In this paper, we have introduced a symmetric non-Hermitian Hamiltonian model which is given as where ω and α are real constants, and are first-order differential operators. The Hermitian form of the Hamiltonian is obtained by suitable mappings and it is interrelated to the time-independent one-dimensional Dirac equation in the presence of position-dependent mass. Then, Dirac equation is reduced to a Schrödinger-like equation and two new complex non- symmetric vector potentials are generated. We have obtained a real spectrum for these new complex vector potentials using the shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.In this paper, we have introduced a symmetric non-Hermitian Hamiltonian model which is given as where ω and α are real constants, and are first-order differential operators. The Hermitian form of the Hamiltonian is obtained by suitable mappings and it is interrelated to the time-independent one-dimensional Dirac equation in the presence of position-dependent mass. Then, Dirac equation is reduced to a Schrödinger-like equation and two new complex non- symmetric vector potentials are generated. We have obtained a real spectrum for these new complex vector potentials using the shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.

arXiv:1301.0205Journal of Physics A Mathematical and TheoreticalDec 3, 20129 citations

One-particle Schrödinger operators

Gerald Teschl

Graduate studies in mathematicsApr 1, 200914 citations

Quantum Mechanics of Complex Sextic Potentials in One Dimension

Aishwarya Parthasarathi, R. S. Kaushal

Within the framework of an extended complex phase space approach characterized by x = x 1 + i p 2 , p = p 1 + i x 2 , we investigate the quasi-exact solutions of an analogous Schrödinger equation for a variety of complex sextic potentials of the type V ( x ) = a + bx + cx 2 + dx 3 + ex 4 + fx 5 + hx 6 with complex couplings. It is found that the eigenvalue spectrum in general is complex for complex couplings and real for the real parameters of the potential. While the ground state solutions for an even power sextic potential with an inverse harmonic term and for the - symmetric version of V ( x ) are obtained, other variants of V ( x ) are also investigated with reference to the excited states.Within the framework of an extended complex phase space approach characterized by x = x 1 + i p 2 , p = p 1 + i x 2 , we investigate the quasi-exact solutions of an analogous Schrödinger equation for a variety of complex sextic potentials of the type V ( x ) = a + bx + cx 2 + dx 3 + ex 4 + fx 5 + hx 6 with complex couplings. It is found that the eigenvalue spectrum in general is complex for complex couplings and real for the real parameters of the potential. While the ground state solutions for an even power sextic potential with an inverse harmonic term and for the - symmetric version of V ( x ) are obtained, other variants of V ( x ) are also investigated with reference to the excited states.

Physica ScriptaJan 1, 200319 citations

COMPLEX HAMILTONIANS HAVING REAL SPECTRA

Carl M. Bender

International Symposium on Quantum Theory and Symmetries (QTS)Jun 1, 20020 citations

\mathcal {PT}

symmetric Hamiltonian model and Dirac equation in 1+1 dimensions