  Mathematical modeling should present a consistent description of physical
phenomena. We illustrate an inconsistency with two Hamiltonians -- the standard
Hamiltonian and an example found in Goldstein -- for the simple harmonic
oscillator and its quantisation. Both descriptions are rich in Lie point
symmetries and so one can calculate many Jacobi Last Multipliers and therefore
Lagrangians. The Last Multiplier provides the route to the resolution of this
problem and indicates that the great debate about the quantisation of
dissipative systems should never have occurred.
