Laplace-Runge-Lenz vector for arbitrary spin

Abstract

A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary spin. The presented systems describe neutral particles with non-trivial multipole momenta. Their spectra can be found algebraically like in the case of Hydrogen atom. Solutions for the systems with spins 1/2 and 1 are presented explicitly, solutions for spin 3/2 are expressed via solutions of an ordinary differential equation of first order..

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References in corpus (7)

• Integrable and superintegrable systems with spin
• Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras
• New exactly solvable systems with Fock symmetry
• Superintegrable systems with spin and second-order integrals of motion
• Quantum superintegrable system for arbitrary spin
• Laplace-Runge-Lenz vector for arbitrary spin
• Superintegrable systems with spin invariant with respect to the rotation group

Cited by in corpus (10)

• Superintegrable systems with position dependent mass
• Superintegrable and shape invariant systems with position dependent mass
• Laplace-Runge-Lenz vector for arbitrary spin
• Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
• Symmetries of Schroedinger equation with scalar and vector potentials
• Laplace-Runge-Lenz vector with spin in any dimension
• 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
• 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