Hamiltonians for systems of N particles interacting through point interactions

G. F. Dell'Antonio; R. Figari; A. Teta

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 60, Issue: 3, page 253-290
  • ISSN: 0246-0211

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Dell'Antonio, G. F., Figari, R., and Teta, A.. "Hamiltonians for systems of N particles interacting through point interactions." Annales de l'I.H.P. Physique théorique 60.3 (1994): 253-290. <http://eudml.org/doc/76635>.

@article{DellAntonio1994,
author = {Dell'Antonio, G. F., Figari, R., Teta, A.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {renormalization techniques of singular quadratic forms; zero-range interactions},
language = {eng},
number = {3},
pages = {253-290},
publisher = {Gauthier-Villars},
title = {Hamiltonians for systems of N particles interacting through point interactions},
url = {http://eudml.org/doc/76635},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Dell'Antonio, G. F.
AU - Figari, R.
AU - Teta, A.
TI - Hamiltonians for systems of N particles interacting through point interactions
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 60
IS - 3
SP - 253
EP - 290
LA - eng
KW - renormalization techniques of singular quadratic forms; zero-range interactions
UR - http://eudml.org/doc/76635
ER -

References

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  1. [1] R.A. Minlos and L.D. Faddeev, On the Point Interaction for a Three-Particle System in Quantum Mechanics, Soviet Phys. Dokl., Vol. 6, 1962, pp. 1072-1074. MR147136
  2. [2] R.A. Minlos and L.D. Faddeev, Comment on the Problem of Three Particles with Point Interactions, Soviet. Phys. Jept., Vol. 14, 1962, pp. 1315-1316. MR151141
  3. [3] S. Albeverio, J.R. Fenstad, R. Hoegh-Krohn, W. Karwowski and T. Lindstrom, Schrödinger Operators with Potentials Supported by Null Sets, To appear in: Ideas and Methods in Quantum and Statistical Physics, S. ALBEVERIO, J. R. FENSTAD, H. HOLDEN, T. LINDSTROM, Eds., Cambridge University Press. Zbl0795.35088MR1190519
  4. [4] E.C. Svendsen, The Effect of Submanifold upon Essential Self-Adjointness and Deficiency Indices, J. Math. Anal. and Appl., Vol. 80, 1981, pp. 551-565. Zbl0473.47039MR614850
  5. [5] S. Albeverio, F. Gesztesy, R. Hoegh-Krohn and H. Holden, Solvable Models in Quantum Mechanics, Springer-Verlag, New-York, 1988. Zbl0679.46057MR926273
  6. [6] A. Teta, Quadratic Forms for Singular Perturbations of the Laplacian, Publ. R.I.M.S. Kyoto Univ., Vol. 26, 1990, pp. 803-817. Zbl0735.35048MR1082317
  7. [7] G. Dal Maso, An Introduction to Γ-Convergence, Preprint S.I.S.S.A., Trieste, 1992. MR1201152
  8. [8] E. De Giorgi, G. Dal Maso, Γ-Convergence and Calculus of Variations. In: Mathematical Theories of Optimization, J. P. CECCONI, T. ZOLEZZI, Eds., Lect. N. in Math., Vol. 979, Springer Verlag, Berlin, 1983. Zbl0511.49007MR713808
  9. [9] K.A. Ter Martirosyan and G.V. Skornyakov, The Three-Body Problem with Short-Range Forces. Scattering of Low-Energy Neutrons by Deuterons, Soviet. Phys. Jept., Vol. 4, 1957, pp. 648-661. Zbl0077.43304MR88334
  10. [10] L.H. Thomas, The Interaction Between a Neutron and a Proton and the Structure of H3, Phys. Rev., Vol. 47, 1935, pp. 903-909. Zbl0011.42701JFM61.1582.02
  11. [11] L.W. Bruch, J.A. Tjon, Binding of Three Identical Bosons in two Dimensions, Phys. Rev. A, Vol. 19, 1979, pp. 425-432. 
  12. [12] T.K. Lim, P.A. Maurone, Non Existence of the Efimov Effect in two Dimensions, Phys. Rev. B, Vol. 22, 1980, pp. 1467-1469. MR582759
  13. [13] R.A. Minlos, M. Sh. SHERMATOV, On Pointlike Interaction of Three Quantum Particles, Vestnik Mosk, Univ. Ser. I Math. Mekh., Vol. 6, 1989, pp. 7-14. Zbl0707.70021MR1065968
  14. [14] R.A. Minlos, On the Point Interaction of Three Particles. In: Applications of Self-Adjoint Extensions in Quantum Physics, Exner, P., Seba, P. Eds., Lect. Notes in Phys., Vol. 324, Springer Verlag, Berlin, 1989. Zbl0738.47008MR1009846
  15. [15] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New-York, 1980. Zbl0521.33001
  16. [16] A. Erdelyi et al., Tables of Integral Transforms, Mc Graw-Hill, New-York, 1954. Zbl0055.36401
  17. [17] D.R. Jafaev, On the Theory of the Discrete Spectrum of the Three-Particle Schrôdinger Operator, Mat. Sb., Vol. 94, 1974, pp. 567-593. Zbl0342.35041MR356752
  18. [18] S.A. Vulgater, G.M. Zhislin, On the Finiteness of the Discrete Spectrum of Hamiltonians for Quantum Systems of Three One-or Two Dimensional Particles, Lett. Math. Phys., Vol. 25, 1992, pp. 299-306. Zbl0759.35033MR1188809
  19. [19] S. Albeverio, R. Høegh-Krohn, T.T. Wu, A Class of Exactly Solvable Three-Body Quantum Mechanical Problems and the Universal Low-Energy Behavior, Phys. Lett., Vol. 83 A, 1981, pp. 105-109. MR617170
  20. [20] J. Dimock, The Non-Relativistic Limit of P(φ)2 Quantum Field Theories: Two-Particle Phenomena, Comm. Math. Phys., Vol. 57, 1977, pp. 51-66. MR475455

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