Unstable quantum oscillator with point interactions: Maverick resonances, antibound states and other surprises
JJ Alvarez, M Gadella, LP Lara… - Physics Letters A, 2013 - Elsevier
In the search for solvable or quasi-solvable models for resonances, we consider a one-
dimensional potential, which is a harmonic oscillator for x< 0, has a point potential at the
origin of the form a δ (x)+ b δ′(x) and no interaction for x> 0. After a study of this model, we
add a mass jump at the origin and study the effect of the combination of the mass jump and
the point potential. We obtain the behavior of resonances, bound and antibound states in
terms of given parameters. In spite of the simplicity of the model, it shows quite interesting …
dimensional potential, which is a harmonic oscillator for x< 0, has a point potential at the
origin of the form a δ (x)+ b δ′(x) and no interaction for x> 0. After a study of this model, we
add a mass jump at the origin and study the effect of the combination of the mass jump and
the point potential. We obtain the behavior of resonances, bound and antibound states in
terms of given parameters. In spite of the simplicity of the model, it shows quite interesting …
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