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On Pointlike Interaction between Three Particles : Two Fermions and Another Particle
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-30
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
The problem of construction of self-adjoint Hamiltonian for quantum system consisting of three pointlike interacting particles (two fermions with mass 1 plus a particle of another nature with mass m>0) was studied in many works.
In most of these works, a family of one-parametric symmetrical operators {Hε,ε∈ℝ1} is considered as such Hamiltonians.
In addition, the question about the self-adjointness of Hε is equivalent to the one concerning the self-adjointness of some auxiliary operators {?l,l=0,1,…} acting in the space L2(ℝ+1,r2dr).
In this work, we establish a simple general criterion of self-adjointness for operators ?l and apply it to the cases l=0 and l=1.
It turns out that the operator ?l=0 is self-adjoint for any m, while the operator ?l=1 is self-adjoint for m>m0, where the value of m0 is given explicitly in the paper.
American Psychological Association (APA)
Minlos, Robert Adol'fovich. 2012. On Pointlike Interaction between Three Particles : Two Fermions and Another Particle. ISRN Mathematical Physics،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-455664
Modern Language Association (MLA)
Minlos, Robert Adol'fovich. On Pointlike Interaction between Three Particles : Two Fermions and Another Particle. ISRN Mathematical Physics No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-455664
American Medical Association (AMA)
Minlos, Robert Adol'fovich. On Pointlike Interaction between Three Particles : Two Fermions and Another Particle. ISRN Mathematical Physics. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-455664
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-455664