$η$-weak-Pseudo-Hermiticity generators and exact solvability

Abstract

Exact solvability of some non-Hermitian $η$-weak-pseudo-Hermitian Hamiltonians is explored as a byproduct of $η$-weak-pseudo-Hermiticity generators. A class of V_{eff}(x)=V(x)+iW(x) potentials is considered, where the imaginary part W(x) is used as an $η$-weak-pseudo-Hermiticity generator to obtain exactly solvable $η$-weak-pseudo-Hermitian Hamiltonian models.