η-weak-pseudo-Hermiticity generators and exact solvability

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 Veff(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