Quantum mechanics from a Heisenberg-type equality
Michael J. W. Hall, Marcel Reginatto
Abstract
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid forall pure states, and is sufficiently strong to provide an axiomatic 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 Schroedinger equation.
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