The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

Albeverio, SergioFassari, SilvestroRinaldi, Fabio2016-02-162016-02-162016-02-16201610.1088/1751-8113/49/2/025302https://infoscience.epfl.ch/handle/20.500.14299/123835WOS:000366675200005In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction, of strength beta, centred at 0 (the bottom of the confining parabolic potential), that was rigorously defined in a previous paper by means of a 'coupling constant renormalisation'. Here we get the Hamiltonian as a norm resolvent limit of the harmonic oscillator Hamiltonian perturbed by a triple of attractive delta-interactions, thus extending the Cheon-Shigehara approximation to the case in which a confining harmonic potential is present.point interactionsperturbed quantum oscillatorsrenormalisationSchrodinger operatorsThe Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactionstext::journal::journal article::research article