Duality of {ital x} and {ital {psi}} and a Statistical Interpretation of Space in Quantum Mechanics

Journal Article · Wed Jan 01 04:00:00 EST 1997 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.78.163· OSTI ID:475295

Faraggi, A E ^[1]; Matone, M ^[2]

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1. Department of Physics, Institute For Fundamental Theory, University of Florida, Gainesville, Florida 32611 (United States)
2. Department of Physics G. Galilei-Istituto Nazionale di Fisica Nucleare, University of Padova, Via Marzolo, 8--35131 Padova (Italy)

We introduce a {open_quotes}prepotential{close_quotes} F in quantum mechanics and show that the coordinate x is proportional to the Legendre transform of F with respect to the probability density. Inversion of the Schr{umlt o}dinger equation leads us to consider an x{endash}{psi} duality related to a modular symmetry. The scaling of x is determined by the {open_quotes}beta function,{close_quotes} suggesting that in quantum mechanics the space coordinate is a macroscopic variable of a statistical system with {h_bar} playing the role of scale. The formalism is extended to higher dimensions and to the Klein-Gordon equation. {copyright} {ital 1997} {ital The American Physical Society}

• Research Organization: University of Florida
• DOE Contract Number: FG05-86ER40272
• OSTI ID: 475295
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 2 Vol. 78; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COORDINATES
DUALITY
KLEIN-GORDON EQUATION
PROBABILITY
QUANTUM MECHANICS
SCALING
SCHROEDINGER EQUATION
SPACE
WAVE FUNCTIONS