**Lie Groups and Quantum Mechanics**

**Abstract:**

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. 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.

[1] Nucci MC & Leach PGL (2007) Gauge Variant Symmetries for the Schrödinger Equation,
*Communications in Mathematical Physics* (submitted)

[2] Nucci MC & Leach PGL (2007) Lagrangians Galore, *Journal of Mathematical Physics*
(submitted)