A complete solution of a constrained system: SUSY monopole quantum mechanics

Abstract

We solve the quantum mechanical problem of a charged particle on S 2 in the background of a magnetic monopole for both bosonic and supersymmetric particles by constructing Hilbert space and realizing the fundamental operators obeying complicated Dirac bracket relations in terms of differential operators. We find the complete energy eigenfunctions. Using the lowest energy eigenstates we count the number of degeneracies and examine the supersymmetry structure of the ground states in detail. © SISSA 2006.