dc.contributor.author | Joseph Akeyo Omolo | |
dc.date.accessioned | 2020-12-01T07:03:44Z | |
dc.date.available | 2020-12-01T07:03:44Z | |
dc.date.issued | 2015 | |
dc.identifier.uri | https://repository.maseno.ac.ke/handle/123456789/3133 | |
dc.description.abstract | The Weber-Hermite differential equation, obtained as the dimensionless form of the stationary
Schroedinger equation for a linear harmonic oscillator in quantum mechanics, has been expressed
in a generalized form through introduction of a constant conjugation parameter according to
the transformation
x x
d d
d d
→ , where the conjugation parameter is set to unity ( = 1 ) at the end
of the evaluations. Factorization in normal order form yields -dependent composite eigenfunctions, Hermite polynomials and corresponding positive eigenvalues, while factorization in the anti-normal order form yields the partner composite anti-eigenfunctions, anti-Hermite polynomials
and negative eigenvalues. The two sets of solutions are related by an -sign reversal conjugation
rule → − . Setting = 1 provides the standard Hermite polynomials and their partner antiHermite polynomials. The anti-Hermite polynomials satisfy a new differential equation, which is
interpreted as the conjugate of the standard Hermite differential equation | en_US |
dc.publisher | Scientific Research Publishing | en_US |
dc.subject | Weber-Hermite Differential Equation, Eigenfunctions, Anti-Eigenfunctions, Hermite, Anti-Hermite, Positive-Negative Eigenvalues | en_US |
dc.title | Composite Hermite and Anti-Hermite Polynomials | en_US |
dc.type | Article | en_US |