Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1997-03-14
Nonlinear Sciences
Chaotic Dynamics
27 pages LaTeX file, no figures, submitted to J.Phys.A:Math.Gen
Scientific paper
We apply the generalized formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates (Robnik 1997, paper I). The generalization is technically almost straightforward but physically quite nontrivial since it yields an infinity of new classes of susy-partner potentials, whose spectra are exactly identical except for the lowest $n+1$ states, if the superpotential is defined in terms of the $(n+1)$-st eigenfunction, with $n=0$ reserved for the ground state. First we show that there are practically no possibilities for shape invariant potentials based on higher excited states. Then we calculate the isospectral partner potentials for the following 1-dim potentials (after separation of variables where appropriate): (i) 3-dim (spherically symmetric) harmonic oscillator, (ii) 3-dim (isotropic) Kepler problem, (iii) Morse potential, (iv) P\"oschl-Teller type I potential, and (v) the 1-dim box potential. In all cases except in (v) we get new classes of solvable potentials. In (v) the partner potential to the box potential is a special case of P\"oschl-Teller type I potential. potentials. In this paper we present results of a straightforward further application of this formalism to a few most important exactly solvable 1-dim potentials, namely (i) spherically symmetric 3-dim harmonic oscillator, (ii) 3-dim isotropic (spherically symmetric) Kepler potential, (iii) Morse potential, (iv) P\"oschl-Teller type I potential, and (v) 1-dim box potential. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.Sq
Liu Jun-xian
Robnik Marko
No associations
LandOfFree
Supersymmetric quantum mechanics based on higher excited states II: a few examples of isospectral partner 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 Supersymmetric quantum mechanics based on higher excited states II: a few examples of isospectral partner potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Supersymmetric quantum mechanics based on higher excited states II: a few examples of isospectral partner potentials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-369927