Skip to main content
SpringerLink
Log in

Semi-classical quantization using the method of harmonic balance

  • Note Brevi
  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

We show, by means of an example, that good estimates can be obtained for the energy levels of one-dimensional quantum systems where the potential has all bound states. The calculation uses a semi-classical expression to determine the energy levels where the classical periodic states are evaluated using the method of harmonic balance.

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. M. Lakshmanan andJ. Prabhakaran:Lett. Nuovo Cimento,7, 689 (1973).

    Article  Google Scholar 

  2. M. Lakshmanan:Lett. Nuovo Cimento,8, 743 (1973).

    Article  MATH  Google Scholar 

  3. S. N. Biswas, K. Datta, R. P. Saxena, P. K. Srivastava andV. S. Varma:J. Math. Phys.,14, 1190 (1973).

    Article  ADS  MATH  Google Scholar 

  4. F. T. Hioe andE. W. Montroll:J. Math. Phys. (N.Y.),16, 1945 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  5. F. T. Hioe, D. MacMillen andE. W. Montroll:J. Math. Phys. (N. Y.),17, 1320 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Martin-Sánchez andJ. Diaz-Bejarano:J. Phys. A,19, 887 (1986).

    Article  Google Scholar 

  7. N. Bessis andG. Bessis:J. Math. Phys. (N.Y.),21, 2780 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  8. A. B. Migdal andV. P. Krainov:Approximation Methods in Quantum Mechanics (W. A. Benjamin, New York, N.Y., 1969).

    Google Scholar 

  9. R. E. Mickens:J. Sound Vib.,94, 456 (1984).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. R. E. Mickens:J. Sound Vib.,111, 515 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  11. V. I. Arnold:Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, N.Y., 1978).

    Book  MATH  Google Scholar 

  12. N. K. Bary:A Treatise on Trigonometric Series, Vol. 1 (MacMillan, New York, N.Y., 1964).

    MATH  Google Scholar 

  13. H. Kisken andH. D. Vollmer:Z. Phys.,201, 323 (1967).

    Article  ADS  Google Scholar 

  14. R. E. Mickens andW. J. Evans:Bull. Am. Phys. Soc.,32, 1091 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, Atlanta University, 30314, Atlanta, Georgia, USA

    R. E. Mickens

Authors
  1. R. E. Mickens
    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

Mickens, R.E. Semi-classical quantization using the method of harmonic balance. Nuov Cim B 101, 359–365 (1988). https://doi.org/10.1007/BF02828714

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02828714

PACS

Search

Navigation