  On the basis of (i) the discrete and continuous symmetries (and corresponding
conserved charges), (ii) the ensuing algebraic structures of the symmetry
operators and conserved charges, and (iii) a few basic concepts behind the
subject of differential geometry, we show that the celebrated
Friedberg-Lee-Pang-Ren (FLPR) quantum mechanical model (describing the motion
of a single non-relativistic particle of unit mass under the influence of the
general spatial 2D rotationally invariant potential) provides a tractable
physical example for the Hodge theory within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism where the symmetry operators and
conserved charges lead to the physical realizations of the de Rham
cohomological operators of differential geometry at the algebraic level. We
concisely mention the Hodge decomposition theorem in the quantum Hilbert space
of states and choose the harmonic states as the real physical states of our
theory. We discuss the physicality criteria w.r.t. the conserved and nilpotent
versions of the (anti-)BRST and (anti-)co-BRST charges and the physical
consequences that ensue from them.
