Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators. I: Integral representation of Kronecker power series and multivariate Hausdorff moment problems

DOI10.1007/s10910-014-0371-8zbMath1306.81048OpenAlexW2004655440MaRDI QIDQ460967

Muzaffer Ayvaz, Metin Demiralp

Publication date: 9 October 2014

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-014-0371-8

zbMATH Keywords

ordinary differential equationsquantum mechanicsHausdorff moment problemexpectation value dynamicsKronecker power seriesprobabilistic evolution approach

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Explicit solutions, first integrals of ordinary differential equations (34A05) Alternative quantum mechanics (including hidden variables, etc.) (81Q65)

Related Items (5)

Promenading in the enchanted realm of Kronecker powers: single monomial probabilistic evolution theory (PREVTH) in evolver dynamics ⋮ Somehow emancipating probabilistic evolution theory (PREVTH) from singularities via getting single monomial PREVTH ⋮ Using enchanted features of constancy adding space extension (CASE) to reduce the dimension of evolver dynamics: single monomial probabilistic evolution theory ⋮ Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators. II: The use of mathematical fluctuation theory ⋮ Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices

Cites Work

• Unnamed Item
• A probabilistic foundation for dynamical systems: theoretical background and mathematical formulation
• A probabilistic foundation for dynamical systems: phenomenological reasoning and principal characteristics of probabilistic evolution
• Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. I: Arbitrariness and equipartition theorem in Kronecker power series
• Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 2: Kernel separability, space extension, and, series solution via telescopic matrices
• Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators. II: The use of mathematical fluctuation theory
• The multidimensional moment problem
• A contemporary linear representation theory for ordinary differential equations: multilinear algebra in folded arrays (folarrs) perspective and its use in multidimensional case
• A contemporary linear representation theory for ordinary differential equations: probabilistic evolutions and related approximants for unidimensional autonomous systems
• A probabilistic evolution approach trilogy. III: Temporal variation of state variable expectation values from Liouville equation perspective
• A probabilistic evolution approach trilogy. II: Spectral issues for block triangular evolution matrix, singularities, space extension

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