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Quantum Fictitious Forces
Author(s) -
BiałynickiBirula I.,
Cirone M.A.,
Dahl J.P.,
Seligman T.H.,
Straub F.,
Schleich W.P.
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<599::aid-prop599>3.0.co;2-g
Subject(s) - physics , classical mechanics , quantum , angular momentum , uncertainty principle , kinetic energy , central force , potential energy , quadratic equation , body force , conservative force , momentum (technical analysis) , bound state , quantum mechanics , mathematics , geometry , finance , economics
We present Heisenberg's equation of motion for the radial variable of a free non‐relativistic particle in D dimensions. The resulting radial force consists of three contributions: (i) the quantum fictitious force which is either attractive or repulsive depending on the number of dimensions, (ii) a singular quantum force located at the origin, and (iii) the centrifugal force associated with non‐vanishing angular momentum. Moreover, we use Heisenberg's uncertainty relation to introduce a lower bound for the kinetic energy of an ensemble of neutral particles. This bound is quadratic in the number of atoms and can be traced back to the repulsive quantum fictitious potential. All three forces arise for a free particle: “Force without force”.