Pauli equation and the method of supersymmetric factorization

Abstract

We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to one-dimensional Darboux transformations. We consider both the case when such factorization is reduced to the ordinary 2-dimensional SUSY QM quasifactorization and a more general case which involves covariant derivatives. The admissible classes of electromagnetic fields are described and some illustrative examples are given.

18 pages, Latex

References in corpus (3)

• Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems
• An application of supersymmetric quantum mechanics to a planar physical system
• Charged spin 1/2 particle in an arbitrary magnetic field in two spatial dimensions: a supersymmetric quantum mechanical system

Cited by in corpus (18)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• SUSY-Approach for Investigation of Two-Dimensional Quantum Mechanical Systems
• SUSY approach to Pauli Hamiltonians with an axial symmetry
• New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models
• Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
• Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics
• Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation
• Analytical Solution of Two-Dimensional Scarf II Model by Means of SUSY Methods
• N-fold Supersymmetry in Quantum Mechanical Matrix Models
• Polynomial Supersymmetry for Matrix Hamiltonians
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Planar Supersymmetric Quantum Mechanics of a Charged Particle in an External Electromagnetic Field
• On two-dimensional supersymmetric quantum mechanics, pseudoanalytic functions and transmutation operators
• Some Properties of the Shape Invariant Two-Dimensional Scarf II Model
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane