TY - JOUR

T1 - Quantum mechanics from a Heisenberg-type equality

AU - Hall, Michael J.W.

AU - Reginatto, Marcel

PY - 2002

Y1 - 2002

N2 - The usual Heisenberg uncertainty relation, ΔX ΔP ≥ ℏ/2, may be replaced by an exact equality for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. This exact uncertainty relation, δX ΔPnc ≡ ℏ/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.

AB - The usual Heisenberg uncertainty relation, ΔX ΔP ≥ ℏ/2, may be replaced by an exact equality for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. This exact uncertainty relation, δX ΔPnc ≡ ℏ/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.

UR - http://www.scopus.com/inward/record.url?scp=0036334016&partnerID=8YFLogxK

U2 - 10.1002/1521-3978(200205)50:5/7<646::AID-PROP646>3.0.CO;2-7

DO - 10.1002/1521-3978(200205)50:5/7<646::AID-PROP646>3.0.CO;2-7

M3 - Article

SN - 0015-8208

VL - 50

SP - 646

EP - 651

JO - Fortschritte der Physik

JF - Fortschritte der Physik

IS - 5-7

ER -