Publication

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

2016
Journal Articles

Abstract

In 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.

Official source

https://infoscience.epfl.ch/entities/publication/ee06bb34-f06a-4928-84ab-0ce3bc5630f9

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2016
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ee06bb34-f06a-4928-84ab-0ce3bc5630f9

About this result

Related concepts (32)

Quantum harmonic oscillator

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known.

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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

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