New Applications of the Biedenharn-temple Operator ( 1)

The Biedenharn approach to the Dirac-Coulomb problem is applied to a system considered by D'Hoker and Vinet, which consists of a spin 1 2 particle in the combined field of a Dirac monopole plus a λ 2 /r 2 potential. The explicit solution is obtained by diagonalizing the 'Biedenharn-Temple operator', Γ. 1. Introduction. In a paper anticipating supersymmetric quantum mechanics, [1], Biedenharn proposed a new approach to the Dirac-Coulomb problem. He starts with the square of the Dirac equation. This equation can be written in a non-relativistic Coulomb form (but with a fractional angular momentum), by using the 'Biedenharn-Temple' [1, 2] operator Γ. The solutions of the first-order equation can be recovered from those of the second-order equation by projection. Recently [3], we have applied Biedenharn's method to the 'dyon' system of D'Hoker and Vinet [4]. Here we illustrate the Biedenharn method on yet another example (also considered by D'Hoker and Vinet [5]), namely that of a spin