Quantum Mechanics from a Heisenberg‐Type Equality

The usual Heisenberg uncertainty relation, ΔX ΔP ≥ h̄/2, may be replaced by an exact equality for suitably chosen measures of position and momentum uncertainty, which is valid for all wave functions. This exact uncertainty relation, δX ΔPnc ≡ h̄/2, can be generalised to other pairs of conjugate observables such as photon number and phase, and is sufficiently strong to provide the basis for moving from classical mechanics to quantum mechanics. In particular, the assumption of a nonclassical momentum fluctuation, having a strength, which scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrödinger equation.