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International Journal of Quantum Chemistry
Article . 2004 . Peer-reviewed
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Isospectral orthogonal polynomials from the Darboux transforms

Authors: J. J. Peña; J. Morales; E. Zamora‐Gallardo; J. García‐Ravelo;

Isospectral orthogonal polynomials from the Darboux transforms

Abstract

AbstractOrthogonal polynomials (OP) are used in many branches of the mathematical and physical sciences; in particular they are part of the eigenfunctions of quantum chemical (QC) potential models. Recently, in the search for new solvable potentials to be useful in QC applications, the use of supersymmetry (SUSY) and Hamiltonian intertwining methods have shown the existence of isospectral potential partners. Also, it has been proved that SUSY is equivalent to the standard Darboux transform (DT) applied to Sturm–Liouville‐type problems. Consequently, because of the similarity between the differential equations of OP and of SL, we consider the application of the standard and generalized DT to find the isospectral OP that are partners of the standard one. To attain this purpose, we use a pair of transformations, a point canonical and a gauge, to convert the SL differential equation into a Schrödinger‐like equation allowing OP solutions. As a useful application of our proposal, we consider some of the most important OP by obtaining the generalized isospectral OP partners. Also, we shown the associated isospectral QC potentials for each of the orthogonal polynomials considered in this work. The proposed procedure can be used to obtain new orthogonal polynomials as well as to find new solvable QC potential models. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Average
Average
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