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Ladder operators for central potential wave functions from the algebraic representation of orthogonal polynomials
Author(s) -
Morales J.,
Peña J. J.,
Sánchez M.,
LópezBonilla J.
Publication year - 1991
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560400818
Subject(s) - laguerre polynomials , hermite polynomials , mathematics , representation (politics) , orthogonal polynomials , wave function , algebraic number , algebra over a field , differential operator , harmonic oscillator , pure mathematics , mathematical analysis , physics , quantum mechanics , politics , political science , law
A general algebraic procedure that yields to raising and lowering operators for the solutions of second‐order differential equations is presented. The method is illustrated by applying it to the differential equations of Hermite and Laguerre polynomials. Taking advantage of the algebraic representation of these polynomials, the ladder operators for harmonic oscillator and hydrogen atom wavefunctions are straightforwardly deduced without resorting to specialized factorizations. The proposed algebraic approach can be extended to the determination of new sets of ladder operators that could be used in the calculation of matrix elements in specific applications.