Closed-form sums for some perturbation series ...
Description
Citation
| Title | Closed-form sums for some perturbation series involving associated Laguerre polynomials |
| Author(s) | R. Hall, N. Saad, A. von Keviczky |
| Journal | Journal of Physics A-Mathematical and General |
| Date | 2001 |
| Volume | 34 |
| Issue | 50 |
| Start page | 11287 |
| End page | 11300 |
| Abstract | Infinite series, Sigma(n=1)(infinity) (alpha/2)(n)/n 1/n! F-1(1)(-n, gamma, x(2)), where F-1(1)(-n, gamma, x(2)) = n!/(gamma)(n) L-n((gamma-1))(x(2)), appear in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H = -d(2)/dx(2) + Bx(2) + A/x(2) + lambda/x(alpha), 0 less than or equal to x 0, A greater than or equal to 0. It is proved that the series is convergent for all x > 0 and 2gamma > alpha where gamma = 1 + 1/2root1+4A. Closed-form sums are presented for these series for the cases alpha = 2, 4 and 6. A general formula for finding the sum for alpha/2 = 2 + m, m = 0, 1, 2.... in terms of associated Laguerre polynomials is also provided. |
| ISSN | 0305-4470 |
Using APA 6th Edition citation style.
[Page generation failure. The bibliography processor requires a browser with Javascript enabled.]
Times viewed: 67
