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Composite Hermite and Anti-Hermite Polynomials

Show simple item record Joseph Akeyo Omolo 2020-12-01T07:03:44Z 2020-12-01T07:03:44Z 2015
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

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