Complex sentence: Potential functions and their parameter sets are in principle "completely arbitrary", as the consistency of a mechanical model is dictated by its Hamiltonian description (see Hamiltonian mechanics) and not by its potential energy term.
Split into simpler sentences: Potential functions and their parameters (when present) are in principle "completely arbitrary". This is true because the consistency of a mechanical model is dictated by its Hamiltonian description (see Hamiltonian mechanics) and not by its potential energy term.