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Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
Odake, Satoru
Sasaki, Ryu
Shape invariance
Orthogonal polynomials
Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite families of the exceptional Laguerre and Jacobi polynomials of types I and II constructed by the present authors. The totality of the integer indices of the new polynomials are finite and they correspond to the degrees of the 'virtual state wavefunctions' which are 'deleted' by the generalisation of Crum-Adler theorem. Each polynomial has another integer n which counts the nodes.
Article
PHYSICS LETTERS B. 702(2-3):164-170 (2011)
ELSEVIER SCIENCE BV
2011-08-11
eng
journal article
AM
http://hdl.handle.net/10091/16121
https://soar-ir.repo.nii.ac.jp/records/11811
https://doi.org/10.1016/j.physletb.2011.06.075
10.1016/j.physletb.2011.06.075
0370-2693
AA00774026
PHYSICS LETTERS B
702
2-3
164
170
https://soar-ir.repo.nii.ac.jp/record/11811/files/Exactly_solvable_quantum_mechanics_infinite_families.pdf
application/pdf
208.9 kB
2015-09-28