We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillator in dimension one, two and three and we study its spectrum. In fact we give a detailed characterization of point spectrum and its asymptotic behavior with respect to the parameters entering the Hamiltonian. We also partially describe the positive spectrum and scattering properties of the Hamiltonian.

Spectral analysis of a two body problem with zero-range perturbation

Correggi, Michele
;
2008

Abstract

We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillator in dimension one, two and three and we study its spectrum. In fact we give a detailed characterization of point spectrum and its asymptotic behavior with respect to the parameters entering the Hamiltonian. We also partially describe the positive spectrum and scattering properties of the Hamiltonian.
2008
Settore MAT/07 - Fisica Matematica
Solvable models in quantum mechanics; zero-range interactions; analysis
File in questo prodotto:
File Dimensione Formato  
Spectral Analysis (CDF).pdf

accesso aperto

Tipologia: Published version
Licenza: Solo Lettura
Dimensione 278.96 kB
Formato Adobe PDF
278.96 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79618
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
  • OpenAlex ND
social impact