${\mathcal N}$-FOLD SUPERSYMMETRIC QUANTUM MECHANICS WITH REFLECTIONS

@article{Tanaka2011mathcalNS,
  title={\$\{\mathcal N\}\$-FOLD SUPERSYMMETRIC QUANTUM MECHANICS WITH REFLECTIONS},
  author={Toshiaki Tanaka},
  journal={International Journal of Modern Physics A},
  year={2011},
  volume={27},
  pages={1250102}
}
  • Toshiaki Tanaka
  • Published 1 December 2011
  • Physics
  • International Journal of Modern Physics A
We formulate -fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of -fold supersymmetry, namely, almost isospectrality and weak quasi-solvability. We construct explicitly the most general one- and two-fold supersymmetric quantum mechanical systems with reflections. In the case of , we find that there are seven inequivalent such systems, three of which are characterized by three arbitrary… 
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6 Citations

6 Citations

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References

SHOWING 1-10 OF 40 REFERENCES

$\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS

We formulate -fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix two-fold supersymmetric quantum mechanical systems. We find that…

{\cal N} -fold supersymmetry in quantum systems with position-dependent mass

We formulate the framework of -fold supersymmetry in one-body quantum mechanical systems with position-dependent mass (PDM). We show that some of the significant properties in the constant-mass case…

N-fold Supersymmetry in Quantum Mechanics - General Formalism -

SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM

In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most…

Nonlinear supersymmetry in quantum mechanics: Algebraic properties and differential representation

Parasupersymmetry and N-fold supersymmetry in quantum many-body systems. I. General formalism and second order

A novel multi-parameter family of quantum systems with partially broken N-fold supersymmetry

We develop a systematic algorithm for constructing an -fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we…

N-fold supersymmetry and quasi-solvability associated with X2-Laguerre polynomials

We construct a new family of quasi-solvable and N-fold supersymmetric quantum systems where each Hamiltonian preserves an exceptional polynomial subspace of codimension 2. We show that the family…

Supersymmetric quantum mechanics with reflections

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is…

Matrix superpotentials

We present a collection of matrix-valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of…