Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-19T04:30:56.023Z Has data issue: false hasContentIssue false
  • English
  • Français

Laguerre functions with truncated domain

Published online by Cambridge University Press:  26 February 2010

Bayard Rankin
Bayard Rankin
Affiliation:
Case Institute of Technology. Cleveland, Ohio, U.S.A., and St. Salvator's College, St. Andrews.
Get access

Extract

We wish to prove a theorem concerning the average values for the functions Ln(2u)e−u, 0 ≤x≤u < ∞, n=0,1,2, …, where Ln is the n-th Laguerre polynomial. Such functions will be called Laguerre functions with domain truncated at x.

Type
Research Article
Information
Mathematika , Volume 13 , Issue 1 , June 1966 , pp. 54 - 56
Copyright
Copyright © University College London 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Groenwold, H. J., “On the principles of elementary quantum mechanics”, Physica, 12 (1946), 405–460.CrossRefGoogle Scholar
2. Bartlett, M. S. and Moyal, J. E., “The exact transition probabilities of quantum mechanical oscillators calculated by the phase-space method”, Proc. Cambridge Phil. Soc., 45 (1949), 545–553.Google Scholar
3. Fairlie, D. B., “The foundations of quantum mechanics in terms of phase space functions”, Proc. Cambridge Phil. Soc., 60 (1964), 581–586.CrossRefGoogle Scholar
4. Rankin, Bayard, “Quantum mechanical time”, J. Mathematical Phys., 6 (1965), 1057–1071.CrossRefGoogle Scholar
5. Rankin, Bayard, “Quantized energy distributions for the harmonic oscillator”, Phys. Rev., 141 (1966), 1223–1230.CrossRefGoogle Scholar