Cyclic Shape Invariant Potentials

Details Cyclic Shape Invariant Potentials Cyclic Shape Invariant Potentials

1997-06-08

arxiv.org/abs/hep-ph/9706282v1

Phys.Lett. A234 (1997) 401-409

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 4 figures

Scientific paper

10.1016/S0375-9601(97)00555-0

We formulate and study the set of coupled nonlinear differential equations which define a series of shape invariant potentials which repeats after a cycle of $p$ iterations. These cyclic shape invariant potentials enlarge the limited reservoir of known analytically solvable quantum mechanical eigenvalue problems. At large values of $x$, cyclic superpotentials are found to have a linear harmonic oscillator behavior with superposed oscillations consisting of several systematically varying frequencies. At the origin, cyclic superpotentials vanish when the period $p$ is odd, but diverge for $p$ even. The eigenvalue spectrum consists of $p$ infinite sets of equally spaced energy levels, shifted with respect to each other by arbitrary energies $\omega_0,\omega_1,\...,\omega_{p-1}$. As a special application, the energy spacings $\omega_k$ can be identified with the periodic points generatedby the logistic map $z_{k+1}=r z_k (1 - z_k)$. Increasing the value of $r$ and following the bifurcation route to chaos corresponds to studying cyclic shape invariant potentials as the period $p$ takes values 1,2,4,8,...

Affiliated with

Also associated with

No associations

Rating

Cyclic Shape Invariant Potentials 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 Cyclic Shape Invariant Potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cyclic Shape Invariant Potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-217760