Journal ArticleDOI
Differential equations in the spectral parameter
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TLDR
In this article, the potentials for the Schrodinger equation (−∂¯¯¯¯ 2 + V(x))∅=k 2 ∅ such that some family of eigenfunctions ∅ satisfies a differential equation in the spectral parameter k of the formB(k, ∂¯¯¯¯ k )o=Θ(x)o.Abstract:
We determine all the potentialsV(x) for the Schrodinger equation (−∂
2
+V(x))∅=k2∅ such that some family of eigenfunctions ∅ satisfies a differential equation in the spectral parameterk of the formB(k, ∂
k
)o=Θ(x)o. For each suchV(x) we determine the algebra of all possible operatorsB and the corresponding functions Θ(x)read more
Citations
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Journal ArticleDOI
Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
TL;DR: In this article, it was shown that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillators.
Journal ArticleDOI
A matrix integral solution to two-dimensional W p -gravity
TL;DR: In this article, it was shown that τ is a vacuum vector generated from the coefficients of the vertex operator, and the connection between the wave function and vertex operator was established via a disguised differential version of the Fay identity, which is also the key to spectral theory for the two compatible symplectic structures of KdV in terms of the stress energy tensor associated with the Virasoro algebra.
Journal Article
Bispectral commutative ordinary differential operators
TL;DR: In this article, the problem of classifying bispectral linear ODEs was studied in connexion with some questions in X-ray tomography, where the objective was to find all possible ODE operators for which there exist ψ and Λ s above satisfying equations of the form
Journal ArticleDOI
Nahm's transformation for instantons
Peter J. Braam,Pierre van Baal +1 more
TL;DR: The Nahm transformation as mentioned in this paper maps anti-self dual connections on the four-torus (S1)4 onto the dual torus (2)4 and shows that this map is a hyper-Kahler isometry.
Journal ArticleDOI
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
TL;DR: In this paper, a constructive supersymmetric quantum mechanical method based on a reparametrization of the corresponding conventional superpotential and on the addition of an extra rational contribution expressed in terms of some polynomial g is proposed.
References
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Book
Infinite Dimensional Lie Algebras
TL;DR: The invariant bilinear form and the generalized casimir operator are integral representations of Kac-Moody algebras and the weyl group as mentioned in this paper, as well as a classification of generalized cartan matrices.
Reference BookDOI
Asymptotics and Special Functions
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
Journal ArticleDOI
Loop groups and equations of KdV type
Graeme Segal,George Wilson +1 more
TL;DR: In this article, the authors decrit une construction qui attribue une solution de l'equation de Korteweg-de Vries a chaque point d'un certain grassmannien de dimension infinie.
Journal ArticleDOI
Monodromy- and spectrum-preserving deformations. I
Hermann Flaschka,Alan C. Newell +1 more
TL;DR: In this paper, a method for solving nonlinear ordinary and partial differential equations with regular and irregular singular points is developed. But the main idea is to study monodromy preserving deformations of linear ordinary differential equations, and the connections with isospectral deformations are discussed.
Journal ArticleDOI
Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt
TL;DR: Auf Veranlassung meines verehrten Kollegen, Herrn A. Stodola, beschaftigte ich mich vor einiger Zeit mit der Frage, wann eine Gleichung n ten Grades with reelle Koeffizienten ist negativ sind as discussed by the authors.
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