Skip to main content
Log in

Applications of hyperdifferential operators to quantum mechanics

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

In this paper, various applications of the theory of hyperdifferential operators to quantum mechanics are discussed. A concise summary of the relevant aspects of the theory is presented, and then used to derive a variety of operator identities, expansions, and solutions to differential equations.

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. Du Chateau, P.: Thesis. Purdue University 1970.

  2. Goldstein, M.E.: J. Math. Phys.11, 667 (1970).

    Google Scholar 

  3. Gel'fand, I., Shilov, G.: Generalized functions. New York: Academic Press 1967.

    Google Scholar 

  4. Hormander, L.: Theory of partial differential equations. Berlin-Göttingen-Heidelberg: Springer 1963.

    Google Scholar 

  5. - Acta Math. to appear.

  6. Kohn, J.J., Nirenberg, L.: Commun. Pure Appl. Math.18, 269–305 (1965).

    Google Scholar 

  7. Kolsrud, M.: J. Math. Phys.11, 829 (1970).

    Google Scholar 

  8. Lambropoulos, P.: J. Math. Phys.8, 2167 (1967).

    Google Scholar 

  9. Mehta, C.L.: J. Math. Phys.5, 677 (1964).

    Google Scholar 

  10. Miller, M.M.: J. Math. Phys.10, 1406 (1969).

    Google Scholar 

  11. Nueringer, J.L.: J. Math. Phys.10, 250 (1969).

    Google Scholar 

  12. Shewell, J.: Am. J. Phys.27, 16 (1959).

    Google Scholar 

  13. Steinberg, S., Treves, F.: J. Diff. Eqns.8, 333 (1970).

    Google Scholar 

  14. Treves, F.: Topological vector spaces, distributions and kernels. New York: Academic Press 1967.

    Google Scholar 

  15. —— Ovcyannikov theorem and hyperdifferential operators. Rio de Janeiro: I.M.P.A. 1969.

    Google Scholar 

  16. —— Bull. Soc. Math. France97, 193 (1969).

    Google Scholar 

  17. Wilcox, R.M.: J. Math. Phys.8, 962 (1967).

    Google Scholar 

  18. —— J. Math. Phys.11, 1235 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was partially supported by N.S.F. grant GP 19614.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miller, M., Steinberg, S. Applications of hyperdifferential operators to quantum mechanics. Commun.Math. Phys. 24, 40–60 (1971). https://doi.org/10.1007/BF01907033

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01907033

Keywords

Navigation