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A Two-Particle Quantum System with Zero-Range Interaction

Michele Correggi[1]

  • [1] CIRM, Fondazione Bruno Kessler Via Sommarive 14 38100 Trento Italy

Séminaire Équations aux dérivées partielles (2008-2009)

  • Volume: 2008-2009, page 1-17

Abstract

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We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.

How to cite

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Correggi, Michele. "A Two-Particle Quantum System with Zero-Range Interaction." Séminaire Équations aux dérivées partielles 2008-2009 (2008-2009): 1-17. <http://eudml.org/doc/11191>.

@article{Correggi2008-2009,
abstract = {We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.},
affiliation = {CIRM, Fondazione Bruno Kessler Via Sommarive 14 38100 Trento Italy},
author = {Correggi, Michele},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {two-particle quantum system; Schrödinger operator; self-adjoint operators; spectral analysis},
language = {eng},
pages = {1-17},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {A Two-Particle Quantum System with Zero-Range Interaction},
url = {http://eudml.org/doc/11191},
volume = {2008-2009},
year = {2008-2009},
}

TY - JOUR
AU - Correggi, Michele
TI - A Two-Particle Quantum System with Zero-Range Interaction
JO - Séminaire Équations aux dérivées partielles
PY - 2008-2009
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2008-2009
SP - 1
EP - 17
AB - We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.
LA - eng
KW - two-particle quantum system; Schrödinger operator; self-adjoint operators; spectral analysis
UR - http://eudml.org/doc/11191
ER -

References

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  10. A. Posilicano, Self-adjoint Extensions of Restrictions, Oper. Matrices2 (2008), 483–506. Zbl1175.47025MR2468877
  11. B. Simon, Trace Ideals and Their Applications, Mathematical Surveys and Monographs 120, American Mathematical Society, Providence, RI, 2005. Zbl1074.47001MR2154153
  12. M. Reed, B. Simon, Methods of Modern Mathematical Physics. Vol I: Functional Analysis, Academic Press, San Diego, 1972. Zbl0242.46001
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  14. M. Reed, B. Simon, Methods of Modern Mathematical Physics. Vol IV: Analysis of Operators, Academic Press, San Diego, 1978. Zbl0401.47001MR493422

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