2000/06/06 by J. C. Lemm, J. Uhlig · 2 citations
Physics and Astronomy · #A priori and a posteriori #Bayes' theorem #Bayesian probability #Bayesian statistics #Cold Atom Physics and Bose-Einstein Condensates #Empirical probability #Field (mathematics) #Inverse #Inverse problem #Quantum, superfluid, helium dynamics #Statistical Mechanics and Entropy #quant-ph
paper · pdf · doi:10.1007/s006010070007
published in Few-Body Systems 29(1-3), 25-52 (Springer Science+Business Media) · LaTex, 32 pages, 19 figures
arxiv created 2000/06/06 · openalex publication_date 2000/11/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The paper presents the basic theory, concentrating in particular on measurements of particle coordinates in quantum mechanical systems at finite temperature. The computational feasibility of the approach is demonstrated by numerical case studies. Finally, it is shown how the approach can be generalized to such many-body and few-body systems for which a mean field description is appropriate. This is done by means of a Bayesian inverse Hartree-Fock approximation.