An Optimal Transport View of Schrödinger's Equation
نویسندگان
چکیده
منابع مشابه
An Optimal Transport View on Schrödinger’s Equation
We show that the Schrödinger equation is a lift of Newton’s third law of motion ∇μ̇ μ̇ = −∇WF (μ) on the space of probability measures, where derivatives are taken w.r.t. the Wasserstein Riemannian metric. Here the potential μ → F (μ) is the sum of the total classical potential energy 〈V, μ〉 of the extended system and its Fisher information ~2 8 ∫ |∇ ln μ|2dμ. The precise relation is established ...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2012
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2011-121-9