Algebraic Realization of Supersymmetric Quantum Mechanics for Cyclic Shape Invariant Potentials

Details Algebraic Realization of Supersymmetric Quantum Mechanics for Cyclic Shape Invariant Potentials Algebraic Realization of Supersymmetric Quantum Mechanics for Cyclic Shape Invariant Potentials

1999-01-22

arxiv.org/abs/math-ph/9901016v1

Helv.Phys.Acta 72 (1999) 71-92

Physics

Mathematical Physics

LaTeX 2e, 22 pages, 8 figures (included)

Scientific paper

We study in detail the spectrum of the bosonic oscillator Hamiltonian associated with the $C_3$-extended oscillator algebra \algthree, where $C_3$ denotes a cyclic group of order three, and classify the various types of spectra in terms of the algebra parameters $\alpha_0, \alpha_1$. In such a classification, we identify those spectra having an infinite number of periodically spaced levels, similar to those of cyclic shape invariant potentials of period three. We prove that the hierarchy of supersymmetric Hamiltonians and supercharges, corresponding to the latter, can be realized in terms of some appropriately chosen \algthree algebras, and of Pauli spin matrices. Extension to period-$\lambda$ spectra in terms of $C_{\lambda}$-extended oscillator algebras is outlined.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-720880