Infinite-dimensional Schrödinger equations with polynomial potentials and Feynman path integrals

DOI10.1134/S1064562406030069zbMath1327.81257MaRDI QIDQ492366

O. G. Smolyanov, Eugene T. Shavgulidze

Publication date: 20 August 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Path integrals in quantum mechanics (81S40) PDEs in connection with quantum mechanics (35Q40)

Related Items (9)

Feynman integrals of functionals of exponential form with a polynomial exponent ⋮ Infinite-dimensional evolution equations and the representation of their solutions in the form of Feynman integrals ⋮ Feynman formulas for semigroups generated by an iterated Laplace operator ⋮ Feynman formula for Schrödinger-type equations with time- and space-dependent coefficients ⋮ Feynman and quasi-Feynman formulas for evolution equations ⋮ Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent ⋮ A fundamental solution to the Schrödinger equation with Doss potentials and its smoothness ⋮ Explicit formula for evolution semigroup for diffusion in Hilbert space ⋮ Hilbert supports of measures on locally convex spaces

Cites Work

• Unnamed Item
• Transformations of Feynman integrals under nonlinear transformations of the phase space
• Note on product formulas for operator semigroups
• Hamiltonian Feynman path integrals via the Chernoff formula

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