A complete solution of a Constrained System: SUSY Monopole Quantum Mechanics

TL;DR

This paper provides a comprehensive solution to the quantum mechanics of a charged particle on a sphere with a magnetic monopole, including supersymmetric cases, by explicitly constructing eigenfunctions and analyzing ground state degeneracies.

Contribution

It offers the first complete solution for both bosonic and supersymmetric monopole quantum mechanics, including explicit eigenfunctions and degeneracy analysis.

Findings

Derived the complete set of energy eigenfunctions.

Counted degeneracies of ground states.

Analyzed supersymmetric structure of ground states.

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 cases 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 supersymmetric structure of the ground states in detail.