Research PapersNo Access

LOWER BOUNDS FOR THE ENERGY OF A MANY-BODY MODEL

A. F. PACHECO

Facultad de Ciencias and BIFI, Universidad de Zaragoza, 50009 Zaragoza, Spain

Search for more papers by this author

and

J. SAÑUDO

Departamento de Física, Universidad de Extremadura, 06071 Badajoz, Spain

Search for more papers by this author

https://doi.org/10.1142/S0218301308010350Cited by:0 (Source: Crossref)

Abstract

The well known and analytically solvable Lipkin–Meshkov–Glick model was devised to test several many-body approximation approaches used in nuclear physics. Here, we use this model to illustrate a method that sets lower bounds for the ground state energy of a quantum Hamiltonian. The idea of the method consists of dividing the Hamiltonian into identical groups of terms that represent subdivisions in the particle population of the system, and then to make an appropriate use of the ground energy of one of these groups. The bounds clearly improve as the size of these groups increases.

Keywords:

PACS: 03.65.-w, 03.65.Ca

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

J. M. Levy-Leblond, J. Math. Phys. 10, 806 (1969), DOI: 10.1063/1.1664909. Crossref, Web of Science, ADS, Google Scholar
L. D. Landau and E. M. Lifshitz , Quantum Mechanics. Non-Relativistic Theory ( Pergamon , New York , 1965 ) . Google Scholar
J. L. Basdevant, A. Martin and J. L. Richard, Nucl. Phys. B 343, 60 (1990), DOI: 10.1016/0550-3213(90)90594-4. Crossref, Web of Science, ADS, Google Scholar
L. Epeleet al., Phys. Lett. A 146, 507 (1990), DOI: 10.1016/0375-9601(90)90395-5. Crossref, Web of Science, ADS, Google Scholar
L. Epeleet al., Physica A 173, 500 (1991), DOI: 10.1016/0378-4371(91)90375-M. Crossref, Web of Science, ADS, Google Scholar
A. Khare and J. M. Richard, J. Phys. A 24, L447 (2001). Google Scholar
R. L. Hall and H. R. Post, Proc. Phys. Soc. London 90, 380 (1967). Google Scholar
F. Calogero and C. Marchioro, J. Math. Phys. 10, 562 (1969), DOI: 10.1063/1.1664877. Crossref, Web of Science, ADS, Google Scholar
S. Kilic and K. Mikelic, Phys. Rev. A 48, 2721 (1993). Crossref, Web of Science, ADS, Google Scholar
H. L. Lipkin, N. Meshkov and A. J. Glick, Nucl. Phys. 62, 188 (1965). Crossref, Web of Science, Google Scholar
N. Meshkov, A. J. Glick and H. J. Lipkin, Nucl. Phys. 62, 199 (1965). Crossref, Web of Science, Google Scholar
A. J. Glick, H. J. Lipkin and N. Meshkov, Nucl. Phys. 62, 211 (1965). Crossref, Web of Science, Google Scholar
P. Ring and P. Schuck , The Nuclear Many-Body Problem ( Springer-Verlag , New York , 1980 ) . Crossref, Google Scholar
J. M. Eisenberg and W. Greiner , Nuclear Theory 3 ( North Holland , Amsterdam , 1985 ) . Google Scholar