On the Spectrum of the Schrdinger Hamiltonian of the One-Dimensional Harmonic Oscillator Perturbed by Two Identical Attractive Point Interactions

In this paper the self-adjoint Hamiltonian of the one-dimensional harmonic oscillator perturbed by two identical attractive point interactions (delta distributions) situated symmetrically with respect to the equilibrium position of the oscillator is rigorously defined by means of its resolvent (Greenʹs function). The equations determining the even and odd eigenvalues of the Hamiltonian are explicitly provided in order to shed light on the behaviour of such energy levels both with respect to the separation distance between the point interaction centres and to the coupling constant.