We introduce a ``prepotential'' 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 Schrödinger equation leads us to consider an x- ψ duality related to a modular symmetry. The scaling of x is determined by the ``beta function,'' suggesting that in quantum mechanics the space coordinate is a macroscopic variable of a statistical system with ħ playing the role of scale. The formalism is extended to higher dimensions and to the Klein-Gordon equation.
DUALITY OF X AND PSI AND A STATISTICAL INTERPRETATION OF SPACE IN QUANTUM MECHANICS - TOPCITE 50+ on SPIRES-HEP.
MATONE, MARCO
1997
Abstract
We introduce a ``prepotential'' 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 Schrödinger equation leads us to consider an x- ψ duality related to a modular symmetry. The scaling of x is determined by the ``beta function,'' suggesting that in quantum mechanics the space coordinate is a macroscopic variable of a statistical system with ħ playing the role of scale. The formalism is extended to higher dimensions and to the Klein-Gordon equation.
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