Skip to main content
SpringerLink
Log in

Hydrogen atom in intense magnetic field

  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The structure of a hydrogen atom situated in an intense magnetic field is investigated. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength,H a ≃5×109G. Fields in excess ofH a are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrödinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrödinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2×1010G and 2×1012 G. It is found that at 2×1012 G the lowest energy eigenvalue is changed from −13.6 eV to about −180 eV in agreement with previous variational computations.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Canuto, V. and Chiu, H. Y.: 1968,Phys. Rev. 173, 1210, 1220 and 229

    Article  ADS  Google Scholar 

  2. Cohen, R., Lodenquai, J., and Ruderman, M.: 1970,Phys. Rev. Letters,25, 467

    Article  ADS  Google Scholar 

  3. Canuto, V.: 1970,Astrophys J. Letters 160, L153.

    Article  ADS  Google Scholar 

  4. Sokolov, A. A. and Ternov, I. M.: 1968,Synchrotron Radiation, Pergamon Press, N. Y., p. 67. In terms of an alternate form of the associated Laguerre polynomials (L kλ )) theI ns areI ns (ξ2)=ξn−s L n n−s (ξ2),n>s;I ns (ξ2)=ξs−n L n n−s (ξ2),s>n.See Quantum Mechanics by L. Landau, and E. M. Lifshitz, Pergamon Press, London (1958), p. 499.

    Google Scholar 

  5. Loudon, R.: 1959,Amer. J. Phys. 27, 649.

    Article  Google Scholar 

  6. Haines, L. K. and Roberts, D. H.: 1969,Amer. J. Phys. 37, 1145.

    Article  Google Scholar 

  7. Yafet, Y., Keyes, R. W., and Adams, E. N.: 1956,J. Phys. Chem. Solids,1, 137.

    Article  Google Scholar 

  8. Handbook of Mathematical Functions, 1966, (AMS 55) U. S. Government Printing Office, Washington, D. C., p. 504.

  9. Schiff, L. I. and Snyder, H.: 1939,Phys. Rev. 55, 59.

    Article  MATH  ADS  Google Scholar 

  10. Hartree, D. R.: 1957,The Calculations of Atomic Structures, John Wiley, p. 86.

Download references

Author information

Author notes

  1. D. C. Kelly

    Present address: Miami University, Oxford, Ohio

Authors and Affiliations

  1. Institute for Space Studies, NASA, Goddard Space Flight Center, New York, N.Y., USA

    V. Canuto & D. C. Kelly

Authors
  1. V. Canuto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. C. Kelly
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Canuto, V., Kelly, D.C. Hydrogen atom in intense magnetic field. Astrophys Space Sci 17, 277–291 (1972). https://doi.org/10.1007/BF00642901

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00642901

Keywords

Search

Navigation