XXXIX Workshop on Geometric Methods in Physics 19.06–25.06.2022
XI School on Geometry and Physics 27.06–1.07.2022
In order to secure the right conditions for our Workshop we have decided to exceptionally move (only for this year's meeting) the site of our Workshop to the campus of our University in Białystok.

David Fernandez


Supersymmetric quantum mechanics and Painleve equations


In the first lecture we will make a brief overview of supersymmetric quantum mechanics (SUSY QM), as a tool for generating new exactly solvable potentials departing from a given initial one. We will illustrate the technique with the harmonic and radial oscillators. In the second lecture we will address the polynomial Heisenberg algebras (PHA), and the way the SUSY partners of the harmonic and radial oscillators realize the even and odd degree PHA respectively. We will explore as well the most general systems ruled by the second and third degree PHA, and the way these systems connect with the Painleve IV (PIV) and V (PV) equations respectively. Finally, in the third lecture we will discuss and algorithm for generating solutions of the PIV and PV equations departing from the harmonic and radial oscillators respectively.

References
  • J.M. Carballo, D.J. Fernandez, J. Negro, L.M. Nieto, Polynomial Heisenberg algebras, J. Phys. A: Math. Gen. 37 (2004) 10349-10362
  • D. Bermudez, D.J. Fernandez, Supersymmetric quantum mechanics and Painleve IV equation, SIGMA 7 (2011) 025
  • D. Bermudez, D.J. Fernandez, Supersymmetric quantum mechanics and Painleve equations, AIP Conf. Proc. 1575 (2014) 50-88
  • D. Bermudez, D.J. Fernandez, J. Negro, Solutions to the Painleve V equation through supersymmetric quantum mechanics, J. Phys. A: Math. Theor. 49 (2016) 335203







Event sponsored by:
University
of Bialystok
University of Bialystok






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