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Quantum Mechanics from a Heisenberg‐type Equality
Author(s) -
Hall Michael J.W.,
Reginatto Marcel
Publication year - 2002
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200205)50:5/7<646::aid-prop646>3.0.co;2-7
Subject(s) - uncertainty principle , momentum (technical analysis) , heisenberg picture , schrödinger equation , position (finance) , classical mechanics , mathematical formulation of quantum mechanics , physics , axiom , quantum mechanics , basis (linear algebra) , schrödinger's cat , mathematics , quantum statistical mechanics , quantum , supersymmetric quantum mechanics , geometry , finance , economics
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 exactuncertainty relation, δX ΔP nc ≡ 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.