Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
By Satoru Odake, Ryu Sasaki. 2011
170 citations recorded by the source corpus.
Abstract 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.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/91fdfeca04aefe67b443caf66ed5c0df76c43c45
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials (2014, background): “The last few years have seen a great deal of activity in the area of exceptional and exceptional discrete orthogonal polynomials (see, for instance, [5, 8, 9, 15], [16] (where the adjective exceptional for this topic was introduced), [17, 18, 19, 20, 21, 26, 29, 30, 32, 36, 37, 39] and the reference”