A note on the existence and \(\hbar\)-dependency of the solution of equations in quantum mechanics

zbMath0861.35089MaRDI QIDQ1912836

Wataru Ichinose

Publication date: 4 May 1997

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationsDirac equationsWeyl symbolsymbol conditions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Initial value problems for PDEs with pseudodifferential operators (35S10)

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Notes on the Feynman path integral for the Dirac equation ⋮ The Continuity of Solutions with Respect to a Parameter to Symmetric Hyperbolic Systems ⋮ Existence and regularity of propagators for multi-particle Schrödinger equations in external fields ⋮ A mathematical theory of the phase space Feynman path integral of the functional ⋮ Notes on the Cauchy problem for the self-adjoint and non-self-adjoint Schrödinger equations with polynomially growing potentials ⋮ On the mathematical formulation of the restricted Feynman path integrals through broken line paths ⋮ The continuity and the differentiability of solutions on parameters to the Schrödinger equations and the Dirac equations ⋮ Unitary propagators for N-body Schrödinger equations in external field ⋮ On the Feynman path integral for the Dirac equation in the general dimensional spacetime ⋮ Unnamed Item

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