Dirac-like Hamiltonians associated to Schrödinger factorizations

Abstract

In this work, we have extended the factorization method of scalar shape-invariant Schrö\-din\-ger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schrödinger equations have been implemented in the Dirac-like shape invariant equations. We have considered also another kind of anti-intertwining operators changing the sign of energy. The Dirac-like Hamiltonians can be obtained from reduction of higher dimensional spin systems. Two examples have been worked out, one obtained from the sphere ${\mathcal{S}}^2$ and a second one, having a non-Hermitian character, from the hyperbolic space ${\mathcal{H}}^2$.

arXiv comment27 pages

References in corpus (8)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Supersymmetric Quantum Mechanics
• Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
• Darboux transformation for a general Dirac equation in two dimensions
• The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration
• Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators
• Dirac-Weyl equation on a hyperbolic graphene surface under perpendicular magnetic fields
• The solutions of Dirac equation on the hyperboloid under perpendicular magnetic fields