SUSY-hierarchy of one-dimensional reflectionless potentials

  title={SUSY-hierarchy of one-dimensional reflectionless potentials},
  author={Sergei P. Maydanyuk},
  journal={Annals of Physics},
  • S. Maydanyuk
  • Published 27 July 2004
  • Mathematics, Physics
  • Annals of Physics

Figures from this paper

New exactly solvable reflectionless potentials of Gamov's type

In this paper, SUSY-hierarchies of one-dimensional potentials with continuous energy spectra are studied. Use of such hierarchies for analysis of reflectionless potentials is substantiated from the

Double complex SUSY-transformations: Deformations of real potentials and their spectral characteristics

In paper approach of double complex SUSY-transformations with not coincident complex energies of transformation is developed, allowing to deform given real potential $V_{1}$ with obtaining exact

Invisible nuclear system

A consecutive formalism and analysis of exactly solvable radial reflectionless potentials with barriers, which in the spatial semiaxis of radial coordinate $r$ have one hole and one barrier, after

Search of a general form of superpotential in hierarchy with discrete energy spectrum

A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of

1 3 0 O ct 2 00 5 Invisible nuclear system

A consecutive formalism and analysis of exactly solvable radial reflectionless potentials with barriers, which in the spatial semiaxis of radial coordinate r have one hole and one barrier, after

Nonlinear Lattice Within Supersymmetric Quantum Mechanics Formalism

In the last decades, the study of nonlinear one dimensional lattices has attracted much attention of the scientific community. One of these lattices is related to a simplified model for the DNA

Method of determination of the most probable coordinate of formation of alpha-particle in alpha-decay

Method of multiple internal reflections (method MIR) in description of $\alpha$-decay of nucleus in the spherically symmetric approximation is presented in paper. In approach MIR the formalism of

Reflectionless Potentials via Complex Potentials

We point out that the complex potentials can be used to construct the reflectionless potentials and two new classes of reflectionless potentials are proposed. In particular, the robustness of these



New exactly solvable Hamiltonians: Shape invariance and self-similarity.

A class of exactly solvable Hamiltonians is further enlarged by examining two new directions: changes of parameters which are different from the previously studied cases of translation and scaling and extending the usual concept of shape invariance in one step to a multistep situation.

Supersymmetry and quantum mechanics

New shape invariant potentials in supersymmetric quantum mechanics

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, the authors obtain a large

Exactly solvable potentials and quantum algebras.

  • Spiridonov
  • Physics, Mathematics
    Physical review letters
  • 1992
A sef of exactly solvable one-dimensional quantum-mechanical potentials is described. If is defined by a finife-difference-differential equation generating in the limiting cases the Rosen-Morse,


Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra.

One-dimensional inverse power reflectionless potentials

A condition, at which the one-dimensional inverse power potential becomes reflectionless during propagation through it of a plane wave, is obtained on the basis of SUSY QM methods. A scattering of a

Resonant tunnelling of a composite particle through a single potential barrier

Some aspects of quantum tunnelling of a composite particle are clarified by a simple model. We calculate the probability that a couple of point particles bound to each other by a square well

The infinite-dimensional dressing dynamical system

Smooth transparent potentials with infinitely many eigenvalues are constructed. These potentials are asymptotically defined from large order Wronskians built up from exponentials.

Inverse Problems

The leading international journal on the theory and practice of inverse problems, inverse methods and computerized inversion of data.