Spectral analysis of a quantum harmonic oscillator coupled to infinitely many scalar bosons

AbstractWe analyze the spectral property of the Hamiltonian for a model of a quantum harmonic oscillator interacting with infinitely many scalar bosons. The Hamiltonian gives an example of perturbation problem of embedded eigenvalues with infinite dimensional Schrödinger's type operators. It is shown explicitly that the embedded eigenvalues of the free (unperturbed) Hamiltonian do not always disappear under the interaction (perturbation) and the disappearance or the stability of the embedded eigenvalues depends on the parameters contained in the Hamiltonian