Hypercyclic Functions for Backward and Bilateral Shift Operators

Abstract For the rational quantum Calogero systems of type A1⊕A2, AD3 and BC3, we explicitly present complete sets of independent conserved charges and their nonlinear algebras. Using intertwining (or shift) operators, we include the extra ‘odd’ charges appearing for integral couplings. Formulæ for the energy eigenstates are used to tabulate the low-level wave functions.

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A decomposition of reducing subspace for shift operators

Tohoku Mathematical Journal ◽

10.2748/tmj/1178229001 ◽

1983 ◽

Vol 35 (3) ◽

pp. 425-440

Author(s):

Shinzō Kawamura

Keyword(s):

Shift Operators ◽

Reducing Subspace

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SUSUSY Quantum Mechanics

International Journal of Modern Physics A ◽

10.1142/s0217751x97000232 ◽

1997 ◽

Vol 12 (01) ◽

pp. 171-176 ◽

Cited By ~ 63

Author(s):

David J. Fernández C.

Keyword(s):

Quantum Mechanics ◽

Shift Operator ◽

Second Order ◽

Parametric Family ◽

First Order ◽

Shift Operators ◽

Exactly Solvable ◽

Exactly Solvable Hamiltonians

The exactly solvable eigenproblems in Schrödinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham–Moses potentials as a particular case.

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Some properties of Wigner coefficients and hyperspherical harmonics

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410003142x ◽

1956 ◽

Vol 52 (3) ◽

pp. 424-430 ◽

Cited By ~ 25

Author(s):

A. P. Stone

Keyword(s):

Angular Momentum ◽

Euclidean Space ◽

Rotation Group ◽

Dimensional Euclidean Space ◽

Hyperspherical Harmonics ◽

Shift Operators ◽

Analytical Relations

ABSTRACTGeneral shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

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Weighted backward shift operators with invariant distributionally scrambled subsets

Annals of Functional Analysis ◽

10.1215/20088752-3802705 ◽

2017 ◽

Vol 8 (2) ◽

pp. 199-210 ◽

Cited By ~ 18

Author(s):

Xinxing Wu ◽

Lidong Wang ◽

Guanrong Chen

Keyword(s):

Shift Operators ◽

Backward Shift

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Basis properties of the p , q -sine functions

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2014.0642 ◽

2015 ◽

Vol 471 (2174) ◽

pp. 20140642 ◽

Cited By ~ 3

Author(s):

Lyonell Boulton ◽

Gabriel J. Lord

Keyword(s):

Shift Operators ◽

The Family ◽

The Subject ◽

Infinite Multiplicity ◽

Sine Functions

We improve the currently known thresholds for basisness of the family of periodically dilated p , q -sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated with this family. These results seal mathematical gaps in the existing literature on the subject.

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