  Motivated by the Nahm's construction, in this paper we present a systematic
construction of Schr\"{o}dinger Hamiltonians for a spin-1/2 particle where the
Berry connection in the ground-state sector becomes the
Bogomolny-Prasad-Sommerfield (BPS) monopole of $SU(2)$ Yang-Mills-Higgs theory.
Our construction enjoys a single arbitrary monotonic function, thereby creating
infinitely many quantum-mechanical models that simulate the BPS monopole in the
space of model parameters.
