Integrability and supersymmetry of Schroedinger-Pauli equations for neutral particles

Abstract

Integrable quantum mechanical systems for neutral particles with spin $\frac{1}{2}$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear physical content. Solutions for three of them are given in explicit form. The related symmetry algebras and superalgebras are discussed. The presented classification is restricted to two-dimensional systems which admit matrix integrals of motion linear in momenta.

22 pages

References in corpus (10)

• Hamiltonians separable in cartesian coordinates and third-order integrals of motion
• Integrable and superintegrable quantum systems in a magnetic field
• Superintegrable Systems with a Third Order Integrals of Motion
• Integrable and superintegrable systems with spin
• New exactly solvable systems with Fock symmetry
• Superintegrable systems with spin and second-order integrals of motion
• Matrix superpotentials and superintegrable systems for arbitrary spin
• Quantum superintegrable system for arbitrary spin
• Generic matrix superpotentials
• Remarks on Multi-Dimensional Conformal Mechanics

Cited by in corpus (10)

• Superintegrable systems with position dependent mass
• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Laplace-Runge-Lenz vector for arbitrary spin
• Superintegrable systems with spin invariant with respect to the rotation group
• Laplace-Runge-Lenz vector with spin in any dimension
• Symmetries of Schroedinger equation with scalar and vector potentials
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger equations
• Symmetries of the Schroedinger-Pauli equation for neutral particles
• Second-order integrals for systems in $E_2$ involving spin