Computational method for determining the bound state oscillator frequency

Document Type : Original Article

Authors

1 Department of physics and engineering sciences, Buein Zahra Technical University

2 Department of physics, Kazakh National University, Farabi ave., 050040, Almaty, Kazakhstan

Abstract

Creation and annihilation operator’s method that is associated with the system was proposed to determine the oscillator frequency of the bound system which consists of two or more particles, as a function of the orbital quantum number, which is the main parameter to describe the interaction between particles that create new bounding systems like charmonium, hyperatoms, pentaquark, etc. Using quantum field theory and quantum electrodynamics methods, we are found that the creation of a bound state occurs if the coupling constant be small, and masses of gauge bosons also be very small in comparison with masses of constituent particles. The modified Hamiltonian (Schrödinger equation) based on the oscillator frequency parameter describes the bound state characteristic such as the mass spectrum, the constituent mass of particles, and binding energy. The method is typically used to solve the relativistic or nonrelativistic Schrödinger equation and to calculate the binding energy or energy eigenvalue of the system for a wide class of potentials allowing the existence of a bound state. The main purpose of this study is to investigate the relationship of the particle binding energy with the oscillator frequency of the Coulomb type potential (or other potentials) bound systems with the nonrelativistic Schrödinger equation.

Keywords

References

[1] V. B. Berestetskii, E. M. Lifshitz, & L. P. Pitaevskii, Quantum Electrodynamics, Pergamon, Oxford, 1982.
[2] J. Beringer, et al., Review of particle physics, Phys. Rev. D: Part. Fields 86, 010001, 2012.
[3] W.E. Caswell, G.P. Lepage, Effective lagrangians for bound state problems in QED, QCD, and other field theories, Physics Letters B, 167(4) 1986,437-442.
[4] M. Dineykhan, et al., Oscillator Representation in Quantum Physics, Springer-Verlag, 1995.
[5] C. Dover, A.Gal, ≡ Hypernuclei, Annals of Physics, 146(2)1983, 309-348.
[6] M.I. Eides, et al., Theory of light hydrogenlike atoms, Physics Reports, 342(2-3) 2001, 63-261.
[7] A. Jahanshir, Di-mesonic molecules mass spectra, Ind. Jour. of Sci. Tech., 10(22) 2017, 10-13.
[8] A. Jahanshir, Mesonic hydrogen mass spectrum in the oscillator representation, Journal of theoretical and applied physics, 3(4) 2010, 10-13.
[9] S. Pal, et al., A study on the ground and excited states of hypernuclei, Physica Scripta, 95(4) 2020, 045301.
[10] C. Samanta et al., Mass formula from light to hypernuclei, arXiv: nucl-th/0602063v1, 2006.
[11] P.A. Zyla, Particle Data Group, Prog. Theor, Exp. Phys, 2020.
Mathematics and Computational Sciences
Volume 2, Issue 2
May 2021
Pages 16-22

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History

  • Receive Date: 03 March 2021
  • Revise Date: 20 April 2021
  • Accept Date: 21 April 2021

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