Self-Adjoint Extensions of the Pauli Equation in the Presence of a Magnetic Monopole

  title={Self-Adjoint Extensions of the Pauli Equation in the Presence of a Magnetic Monopole},
  author={Edwin Richard Karat and Michael B. Schulz},
  journal={Annals of Physics},
Abstract We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However… 
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Relativistic Quantum Mechanics. Wave Equations
1. Relativistic Wave Equation for Spin-0 Particles: The Klein-Gordon Equation and Its Applications.- 2. A Wave Equation for Spin-1/2 Particles: The Dirac Equation.- 3. Lorentz Covariance of the Dirac
Methods of Mathematical Physics
The following people have maintained these notes.
  • J. Mod. Phys. A5
  • 1990
Relativistic Quantum Mechanics: Wave Equations (Springer-Verlag
  • New York),
  • 1994
Quantum Electodynamics
  • Quantum Electodynamics
  • 1989
Quantum Electodynamics ( Pergamon , New York ) , 130 [ 6 ] E . Farhi and S . Gutmann
  • 1989
Quantum Electodynamics ( Pergamon , New York ) , 130 [ 6 ] H . Narnhofer
  • Acta Physica Austriaca
  • 1989
and L
  • Pitaevskii
  • 1989
Coleman in Magnetic Monopole – 50 years later , from International School of Subnuclear Physics
  • HUTP-82/A032)
  • 1981
C. J. Callias, Phys. Rev
  • C. J. Callias, Phys. Rev
  • 1977