Matrix superpotentials and superintegrable systems for arbitrary spin

Abstract

A countable set of quantum superintegrable systems for arbitrary spin is solved explicitly using tools of supersymmetric quantum mechanics. It is shown that these systems (introduced by Pronko, J. Phys. A: Math. Theor. 40 (2007) ) include matrix shape invariant potentials classified recently in A. G. Nikitin and Y. Karadzhov, J. Phys. A: 44 (2011) 305204; J. Phys. A: 44 (2011) 445202.

15 pages

References in corpus (4)

• Integrable and superintegrable systems with spin
• SUSY approach to Pauli Hamiltonians with an axial symmetry
• Quantum superintegrable system for arbitrary spin
• SU(2) Symmetry and Degeneracy From SUSY QM of a Neutron in the Magnetic Field of a Linear Current

Cited by in corpus (13)

• Superintegrable systems with position dependent mass
• Symmetries and solutions of field equations of axion electrodynamics
• Integrability and supersymmetry of Schroedinger-Pauli equations for neutral particles
• Laplace-Runge-Lenz vector for arbitrary spin
• Symmetries of Schroedinger equation with scalar and vector potentials
• Symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger equations
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups
• Symmetries of the Schroedinger-Pauli equation for neutral particles
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 2. Systems with dilatation and shift symmetries
• Superintegrability in the interaction of two particles with spin