Skip to main content

An orthonormal regularized Lagrange mesh for bound and scattering states

Abstract.

A regularized Lagrange mesh based on exactly orthonormal Lagrange-Laguerre functions is devised and applied to the study of bound states for two solvable radial potentials: the harmonic-oscillator and Coulomb potentials. The analysis of these results and a comparison with calculations based on other Lagrange meshes provide an explanation on the low accuracy of some Lagrange-mesh calculations in the presence of singularities in the potential. Although based on square-integrable functions, this Lagrange mesh can also be used for studying the elastic scattering, by means of integral relations. This approach is tested on two typical examples. Very accurate results are obtained with small numbers of mesh points.

This is a preview of subscription content, access via your institution.

References

  1. D. Baye, P.-H. Heenen, J. Phys. A: Math. Gen. 19, 2041 (1986)

    ADS  Article  Google Scholar 

  2. D. Baye, Phys. Rep. 565, 1 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  3. D. Baye, M. Hesse, M. Vincke, Phys. Rev. E 65, 026701 (2002)

    ADS  MathSciNet  Article  Google Scholar 

  4. M. Vincke, L. Malegat, D. Baye, J. Phys. B: At. Mol. Opt. Phys. 26, 811 (1993)

    ADS  Article  Google Scholar 

  5. M. Hesse, Phys. Rev. E 65, 046703 (2002)

    ADS  Article  Google Scholar 

  6. P. Barletta, C. Romero-Redondo, A. Kievsky, M. Viviani, E. Garrido, Phys. Rev. Lett. 103, 090402 (2009)

    ADS  Article  Google Scholar 

  7. A. Kievsky, M. Viviani, P. Barletta, C. Romero-Redondo, E. Garrido, Phys. Rev. C 81, 034002 (2010)

    ADS  Article  Google Scholar 

  8. A. Kievsky, M. Viviani, L.E. Marcucci, Phys. Rev. C 85, 014001 (2012)

    ADS  Article  Google Scholar 

  9. G. Szegö, Orthogonal Polynomials (American Mathematical Society, Providence, RI, 1975)

  10. V. Szalay, J. Chem. Phys. 99, 1978 (1993)

    ADS  Article  Google Scholar 

  11. D. Baye, J. Phys. A: Math. Theor. 44, 395204 (2011)

    MathSciNet  Article  Google Scholar 

  12. C. Eckart, Phys. Rev. 35, 1303 (1930)

    ADS  Article  Google Scholar 

  13. V. Bargmann, Rev. Mod. Phys. 21, 488 (1949)

    ADS  Article  Google Scholar 

  14. B. Buck, H. Friedrich, C. Wheatley, Nucl. Phys. A 275, 246 (1977)

    ADS  Article  Google Scholar 

  15. M. Hesse, J.-M. Sparenberg, F. Van Raemdonck, D. Baye, Nucl. Phys. A 640, 37 (1998)

    ADS  Article  Google Scholar 

  16. D. Baye, L. Filippin, M. Godefroid, Phys. Rev. E 89, 043305 (2014)

    ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jérémy Dohet-Eraly.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dohet-Eraly, J. An orthonormal regularized Lagrange mesh for bound and scattering states. Eur. Phys. J. Plus 132, 362 (2017). https://doi.org/10.1140/epjp/i2017-11648-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11648-8