The Vladimirov operator with variable coefficients on finite adeles and the Feynman formulas for the Schrödinger equation

We construct the Hamiltonian Feynman, Lagrangian Feynman, and Feynman–Kac formulas for the solution of the Cauchy problem with the Schrödinger operator −MgDα − V, where Dα is the Vladimirov operator and Mg is the operator of multiplication by a real-valued function g defined on the d-dimensional spa...

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Bibliographic Details
Published in:Journal of mathematical physics 2024-04, Vol.65 (4)
Main Author: Urban, Roman
Format: Article
Language:English
Subjects:
Cauchy problems
Hamiltonian functions
Mathematical analysis
Multiplication
Number theory
Operators (mathematics)
Schrodinger equation
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Summary:We construct the Hamiltonian Feynman, Lagrangian Feynman, and Feynman–Kac formulas for the solution of the Cauchy problem with the Schrödinger operator −MgDα − V, where Dα is the Vladimirov operator and Mg is the operator of multiplication by a real-valued function g defined on the d-dimensional space AKd of finite adeles over the algebraic number field K.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0154726