Skip to main content
Log in

A class of solvable potentials

  • Published:
Il Nuovo Cimento (1955-1965)

Summary

The problem of the construction of solvable one-variable Schrödinger potentials is formulated. A class of simple potentials for which the Schrödinger equation can be solved in terms of special functions of physics is constructed.

Riassunto

Si formula il problema della costruzione di potenziali di Schrödinger ad una variabile risolubili. Si costruisce una classe di potenziali semplici per cui l’equazione di Schrödinger può essere risolta in termini di speciali funzioni della fisica.

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

Literatur

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. A. Bhattacharjie andE. C. G. Sudarshan:Nuovo Cimento,25, 864 (1962).

    Article  MathSciNet  Google Scholar 

  3. A. K. Bose:Phys. Lett.,7, 245 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  4. E. G. C. Poole:Introduction to the Theory of Differential Equations (New York, 1960), Sect.28.

  5. A. Erdélyi:Higher Transcendental Functions, Vol.1 (New York, 1953), Sect. 2.6; reference (3), Sect.21.

  6. E. T. Whittaker andG. N. Watson:A Course of Modern Analysis (Cambridge, 1958), Sect.16.1.

  7. E. L. Ince:Ordinary Differential Equations (New York, 1956), Sect.13.8;L. Bieberbach:Theorie der gewöhnlichen Differentialgleichungen (Berlin, 1953), Sect.4–5.

  8. E. Eckart:Phys. Rev.,35, 1303 (1930).

    Article  ADS  Google Scholar 

  9. L. Hulthén andM. Sugawara:Encyclopedia of Physics, Vol.39 (Berlin, 1959), Sect.12.

  10. R. D. Woods andD. S. Saxon:Phys. Rev.,95, 577 (1954).

    Article  ADS  Google Scholar 

  11. G. Pöschl andE. Teller:Zeits. Phys.,83, 143 (1933).

    Article  ADS  Google Scholar 

  12. F. Reiche:Zeits. Phys.,39, 444 (1926);H. Margenau andG. M. Murphy:The Mathematics of Physics and Chemistry (Princeton, 1956), p. 368.

    Article  ADS  Google Scholar 

  13. N. Rosen andP. M. Morse:Phys. Rev.,42, 210 (1932).

    Article  ADS  Google Scholar 

  14. Reference (3), Sect.21.

  15. Reference (3), Sect.25.

  16. L. D. Landau andE. M. Lifshitz:Quantum Mechanics (London, 1958).S. Flügge andH. Marschall:Rechenmethoden der Quantentheorie, Erster Teil (Berlin, 1952).

  17. R. Jost:Helv. Phys. Acta,20, 256 (1947).

    MathSciNet  MATH  Google Scholar 

  18. Reference (5), Sect.10.6.

  19. A. R. Forsyth:Theory of Differential Equations, Vol.4 (New York, 1959), Sect.54.

  20. A. Messiah:Mécanique Quantique, Chap. VI, Tome 1 (Paris, 1962), Sect.7.

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported in part by the National Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bose, A.K. A class of solvable potentials. Nuovo Cim 32, 679–688 (1964). https://doi.org/10.1007/BF02735890

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02735890

Navigation