In many texts, the transition from classical mechanics to quantum mechanics is achieved by
substituting the action for the phase angle. The paper presents a different approach to show some
connections between classical and quantum mechanics for a single particle for an audience at
graduate and postgraduate levels. Firstly, it is shown that a wave equation of action can be derived
under the free particle condition and the Legendre transform. The wave-like solutions of the action,
Hamiltonian and momentum of the free particle are presented. Using the discrete approximation, the
equation of motion of a single particle, in scalar potential field, is obtained in a similar form to
Schrödinger’s equation. The rest of the paper discusses the propagation, superposition of the
wave-like dynamic variables and their connections to quantum mechanics. The superposition of the
variables of a particle is generally distinct from the superposition of classical waves (e.g.
acoustics). The quantum …