New Possibilities of Harmonic Oscillator Basis Application for Quantum System Description. Two Particles with Coulomb Interaction
Affiliation(s)
1 Department of Applied Informatics, Vytautas Magnus University, Kaunas, Lithuania. 2 Department of Physics, Vytautas Magnus University, Kaunas, Lithuania.
1 Department of Applied Informatics, Vytautas Magnus University, Kaunas, Lithuania. 2 Department of Physics, Vytautas Magnus University, Kaunas, Lithuania.
ABSTRACT
This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.
This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.
KEYWORDS
Harmonic Oscillator Basis, Spurious States, Variational Method, Quantum Systems with Coulomb Potential
Harmonic Oscillator Basis, Spurious States, Variational Method, Quantum Systems with Coulomb Potential
Cite this paper
Deveikis, A. and Kamuntavičius, G. (2015) New Possibilities of Harmonic Oscillator Basis Application for Quantum System Description. Two Particles with Coulomb Interaction. Journal of Modern Physics, 6, 403-413. doi: 10.4236/jmp.2015.64044.
Deveikis, A. and Kamuntavičius, G. (2015) New Possibilities of Harmonic Oscillator Basis Application for Quantum System Description. Two Particles with Coulomb Interaction. Journal of Modern Physics, 6, 403-413. doi: 10.4236/jmp.2015.64044.
References
[1] Kamuntavicius, G.P. (2014) Journal of Mathematical Physics, 55, Article ID: 042103.
http://dx.doi.org/10.1063/1.4870617 [2] Friedrich, H.S. (2005) Theoretical Atomic Physics. 3rd Edition, Springer, Berlin. [3] Faddeev, L.D. (1961) Soviet Physics JETP, 12, 1014-1019. [4] Yakubovsky, O.A. (1967) Soviet Journal of Nuclear Physics, 5, 937-951. [5] Kamuntavicius, G.P. (1986) Few-Body Systems, 1, 91-109.
http://dx.doi.org/10.1007/BF01277077 [6] Kamuntavicius, G.P. (1989) Soviet Journal Particles and Nuclei, 20, 109-140. [7] Deveikis, A. and Kamuntavicius, G.P. (1995) Lithuanian Journal of Physics, 35, 14-19. [8] Deveikis, A. and Kamuntavicius, G.P. (1996) Lithuanian Journal of Physics, 36, 83-95. [9] Navratil, P. and Barrett, B.R. (1996) Physical Review C, 54, 2986-2995.
http://dx.doi.org/10.1103/PhysRevC.54.2986 [10] Deveikis, A. and Kamuntavicius, G.P. (1997) Lithuanian Journal of Physics, 37, 371-383. [11] Navratil, P. and Barrett, B.R. (1998) Physical Review C, 57, 3119-3128.
http://dx.doi.org/10.1103/PhysRevC.57.3119 [12] Navratil, P., Kamuntavicius, G.P. and Barrett, B.R. (2000) Physical Review C, 61, Article ID: 044001.
http://dx.doi.org/10.1103/PhysRevC.61.044001 [13] Racah, G. (1943) Physical Review, 63, 367-382.
http://dx.doi.org/10.1103/PhysRev.63.367 [14] Fano, U. and Racah, G. (1959) Irreducible Tensorial Sets. Academic Press, New York. [15] Schmid, K.W. (2001) The European Physical Journal A, 12, 29-40.
http://dx.doi.org/10.1007/s100500170036 [16] Hagen, G., Papenbrock, T. and Dean, D.J. (2009) Physical Review Letters, 103, Article ID: 062503.
http://dx.doi.org/10.1103/PhysRevLett.103.062503 [17] Hagen, G., Papenbrock, T., Dean, D.J. and Hjorth-Jensen, M. (2010) Physical Review C, 82, Article ID: 034330.
http://dx.doi.org/10.1103/PhysRevC.82.034330 [18] Messud, J. (2013) Physical Review C, 87, Article ID: 024302.
http://dx.doi.org/10.1103/PhysRevC.87.024302 [19] Moshinsky, M. (1969) The Harmonic Oscillator in Modern Physics: From Atoms to Quarks. Gordon and Breach, New York. [20] Kamuntavicius, G.P., Kalinauskas, R.K., Barrett, B.R., Mickevicius, S. and Germanas, D. (2001) Nuclear Physics A, 695, 191-201.
http://dx.doi.org/10.1016/S0375-9474(01)01101-0 [21] Abramowitz, M. and Stegun, I.A. (1972) Handbook of Mathematical Functions. 9th Edition, National Bureau of Standards, Washington DC. [22] Varshalovich, D.A., Moskalev, A.N. and Khersonskii, V.K. (1988) Quantum Theory of Angular Momentum. World Scientific, Singapore.
http://dx.doi.org/10.1142/0270 [23] Gloeckner, D.H. and Lawson, R.D. (1974) Physics Letters B, 53, 313-318.
http://dx.doi.org/10.1016/0370-2693(74)90390-6 [24] Maris, P., Vary, J.P. and Shirokov, A.M. (2009) Physical Review C, 79, Article ID: 014308.
http://dx.doi.org/10.1103/PhysRevC.79.014308 [25] Fernandez-Menchero, L. and Summers, H.P. (2013) Physical Review A, 88, Article ID: 022509.
http://dx.doi.org/10.1103/PhysRevA.88.022509
[1] Kamuntavicius, G.P. (2014) Journal of Mathematical Physics, 55, Article ID: 042103.
http://dx.doi.org/10.1063/1.4870617 [2] Friedrich, H.S. (2005) Theoretical Atomic Physics. 3rd Edition, Springer, Berlin. [3] Faddeev, L.D. (1961) Soviet Physics JETP, 12, 1014-1019. [4] Yakubovsky, O.A. (1967) Soviet Journal of Nuclear Physics, 5, 937-951. [5] Kamuntavicius, G.P. (1986) Few-Body Systems, 1, 91-109.
http://dx.doi.org/10.1007/BF01277077 [6] Kamuntavicius, G.P. (1989) Soviet Journal Particles and Nuclei, 20, 109-140. [7] Deveikis, A. and Kamuntavicius, G.P. (1995) Lithuanian Journal of Physics, 35, 14-19. [8] Deveikis, A. and Kamuntavicius, G.P. (1996) Lithuanian Journal of Physics, 36, 83-95. [9] Navratil, P. and Barrett, B.R. (1996) Physical Review C, 54, 2986-2995.
http://dx.doi.org/10.1103/PhysRevC.54.2986 [10] Deveikis, A. and Kamuntavicius, G.P. (1997) Lithuanian Journal of Physics, 37, 371-383. [11] Navratil, P. and Barrett, B.R. (1998) Physical Review C, 57, 3119-3128.
http://dx.doi.org/10.1103/PhysRevC.57.3119 [12] Navratil, P., Kamuntavicius, G.P. and Barrett, B.R. (2000) Physical Review C, 61, Article ID: 044001.
http://dx.doi.org/10.1103/PhysRevC.61.044001 [13] Racah, G. (1943) Physical Review, 63, 367-382.
http://dx.doi.org/10.1103/PhysRev.63.367 [14] Fano, U. and Racah, G. (1959) Irreducible Tensorial Sets. Academic Press, New York. [15] Schmid, K.W. (2001) The European Physical Journal A, 12, 29-40.
http://dx.doi.org/10.1007/s100500170036 [16] Hagen, G., Papenbrock, T. and Dean, D.J. (2009) Physical Review Letters, 103, Article ID: 062503.
http://dx.doi.org/10.1103/PhysRevLett.103.062503 [17] Hagen, G., Papenbrock, T., Dean, D.J. and Hjorth-Jensen, M. (2010) Physical Review C, 82, Article ID: 034330.
http://dx.doi.org/10.1103/PhysRevC.82.034330 [18] Messud, J. (2013) Physical Review C, 87, Article ID: 024302.
http://dx.doi.org/10.1103/PhysRevC.87.024302 [19] Moshinsky, M. (1969) The Harmonic Oscillator in Modern Physics: From Atoms to Quarks. Gordon and Breach, New York. [20] Kamuntavicius, G.P., Kalinauskas, R.K., Barrett, B.R., Mickevicius, S. and Germanas, D. (2001) Nuclear Physics A, 695, 191-201.
http://dx.doi.org/10.1016/S0375-9474(01)01101-0 [21] Abramowitz, M. and Stegun, I.A. (1972) Handbook of Mathematical Functions. 9th Edition, National Bureau of Standards, Washington DC. [22] Varshalovich, D.A., Moskalev, A.N. and Khersonskii, V.K. (1988) Quantum Theory of Angular Momentum. World Scientific, Singapore.
http://dx.doi.org/10.1142/0270 [23] Gloeckner, D.H. and Lawson, R.D. (1974) Physics Letters B, 53, 313-318.
http://dx.doi.org/10.1016/0370-2693(74)90390-6 [24] Maris, P., Vary, J.P. and Shirokov, A.M. (2009) Physical Review C, 79, Article ID: 014308.
http://dx.doi.org/10.1103/PhysRevC.79.014308 [25] Fernandez-Menchero, L. and Summers, H.P. (2013) Physical Review A, 88, Article ID: 022509.
http://dx.doi.org/10.1103/PhysRevA.88.022509