Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

We find supersymmetric partners of a family self-adjoint operators which are extensions the differential operator −d2/dx2 on L2[−a,a], a>0, that is, one dimensional infinite square well. First all, we classify these in terms several choices parameters determining each extensions. There essentially two big groups In one, ground state has strictly positive energy. On other, either zero or negative present paper, show belonging to first group (energy positive) an sequence partners, such ℓ-th order partner differs energy level from both (ℓ−1)-th and (ℓ+1)-th partners. general, eigenvalues for come transcendental equation all infinite. For case under our study, determine eigenvalues, also infinite, have purely discrete spectrum, their respective eigenfunctions its extension.