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 -