Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry

We have obtained the metric operator $\mathrm{\Theta }=\exp T$ for the non-Hermitian Hamiltonian model $H=\omega (a^{\mathrm{†}}a+1\mathrm{/}2)+\alpha (a^2-a^{{\mathrm{†}}^2})$. We have also found the intertwining operator which connects the Hamiltonian to the adjoint of its pseudo-supersymmetric partner Hamiltonian for the model of hyperbolic Rosen-Morse II potential.