In the context of non-Hermitian quantum mechanics, many systems are known to possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related to its adjoint H^{†} via the relation, H^{†}=PTHPT . We propose a derivation of pseudo PT symmetry and η -pseudo-Hermiticity simultaneously for the time dependent non-Hermitian Hamiltonians by intoducing a new metric η(t)=PTη(t) that not satisfy the time-dependent quasi-Hermiticity relation but obeys the Heisenberg evolution equation. Here, we solve the SU(1,1) time-dependent non-Hermitian Hamiltonian and we construct a time-dependent solutions by employing this new metric and discuss a concrete physical applications of our results.In the context of non-Hermitian quantum mechanics, many systems are known to possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related to its adjoint H^{†} via the relation, H^{†}=PTHPT . We propose a derivation of pseudo PT symmetry and η -pseudo-Hermiticity simultaneously for the time dependent non-Hermitian Hamiltonians by intoducing a new metric η(t)=PTη(t) that not satisfy the time-dependent quasi-Hermiticity relation but obeys the Heisenberg evolution equation. Here, we solve the SU(1,1) time-dependent non-Hermitian Hamiltonian and we construct a time-dependent solutions by employing this new metric and discuss a concrete physical applications of our results.

arXiv:2308.13834Aug 26, 20230 citations

Non-Hermitian Hamiltonians in Quantum Physics

Fabio Bagarello, Roberto Passante, Camillo Trapani

Springer proceedings in physicsJan 1, 2016111 citations

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- $\mathcal{PT}$ -symmetrySpherical-separability of Non-Hermitian Hamiltonians and Pseudo- $\mathcal{PT}$ -symmetry

Omar Mustafa, S. Habib Mazharimousavi

arXiv:0711.3887International Journal of Theoretical PhysicsJul 21, 20083 citations

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo-

\mathcal{PT}

-symmetry