Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials

Details Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials

2004-10-11

arxiv.org/abs/hep-th/0410109v2

J.Math.Phys. 46 (2005) 063513

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 1 figure. The outline of derivation of the result in section 2 is added

Scientific paper

10.1063/1.1927080

We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with five parameters. The corresponding single particle quantum version, which is a typical example of "discrete" quantum mechanical systems with a q-shift type kinetic term, is shape invariant and the eigenfunctions are the Askey-Wilson polynomials. This is an extension of our previous study [1,2], which established the "discrete analogue" of the well-known fact; The equilibrium positions of the Calogero systems are described by the Hermite and Laguerre polynomials, whereas the corresponding single particle quantum versions are shape invariant and the eigenfunctions are the Hermite and Laguerre polynomials.

Affiliated with

Also associated with

No associations

Rating

Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-714692