15 research outputs found
Supercharge Operator of Hidden Symmetry in the Dirac Equation
As is known, the so-called Dirac -operator commutes with the Dirac
Hamiltonian for arbitrary central potential . Therefore the spectrum is
degenerate with respect to two signs of its eigenvalues. This degeneracy may be
described by some operator, which anticommutes with . If this operator
commutes with the Dirac Hamiltonian at the same time, then it establishes new
symmetry, which is Witten's supersymmetry. We construct the general
anticommuting with operator, which under the requirement of this symmetry
unambiguously select the Coulomb potential. In this particular case our
operator coincides with that, introduced by Johnson and Lippmann many years
ago.Comment: 3 page