A position dependent mass Hamiltonian and abstract ladder operators

Abstract We consider the Hamiltonian H of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called abstract ladder operators , in the attempt to find its eigenvalues and eigenvectors. We do not assume that H is self-adjoint, while we focus on the case of a factorizable operator. We show then that pseudo-bosonic operators play a relevant role in this analysis, and we construct bi-coherent states attached to these operators. Explicit examples are discussed.