Skip to main content
Log in

An investigation of the reliability of the Galerkin-Petrov method with a special study of the helium atom ground state

  • Original Investigations
  • Published:
Theoretica chimica acta Aims and scope Submit manuscript

Abstract

A convergence characterization of the Galerkin-Petrov method by means of quantities characterizing pairs of subspaces is presented. The usefulness of our approach for setting up reliable computational schemes is demonstrated for the He atom ground state. Several methods of constructing pairs of subspaces for use in quantum chemistry are suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hegyi, M. G., Mezei, M., Szondy, T. Theoret. Chim. Acta (Berl.) 15, 273, 283 (1969); 21, 168 (1971)

    Google Scholar 

  2. Krasnoselskij, M. A. et al.: Approximate solutions to operator equations. Moskva: Nauka 1969 (in Russian)

    Google Scholar 

  3. Schwartz, C.: J. Comp. Phys. 2, 90 (1967)

    Google Scholar 

  4. Bangudu, E. A., Jankowski, K., Dion, D. R.: Chem. Phys. Letters 19, 418 (1973)

    Google Scholar 

  5. Armour, E. A. G.: Mol. Phys. 25, 993 (1973)

    Google Scholar 

  6. Jankowski, K.: Intern. J. Quantum Chem. 10, 683 (1976)

    Google Scholar 

  7. Wilkinson, J. H.: The algebraic eigenvalue problem. Oxford: Clarendon Press 1965

    Google Scholar 

  8. Löwdin, P. O.: Advan. Chem. Phys. 2, 207 (1959)

    Google Scholar 

  9. Löwdin, P. O.: Phys. Rev. 139, A357 (1965)

    Google Scholar 

  10. Røeggen, I., Huggett, J. P., Armour, E. A. G.: Theoret. Chim. Acta (Berl.) 39, 161 (1975)

    Google Scholar 

  11. Sims, J. S., Hagstrom, S. A.: Phys. Rev. 4A, 908 (1971)

    Google Scholar 

  12. Sims, J. S., Hagstrom, S. A.: J. Chem. Phys. 55, 4699 (1971)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jankowski, K., Rutkowski, A. An investigation of the reliability of the Galerkin-Petrov method with a special study of the helium atom ground state. Theoret. Chim. Acta 43, 145–159 (1976). https://doi.org/10.1007/BF00547254

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00547254

Key words

Navigation