Derivation and application of extended parabolic wave theories. II. Path integral representations

DOI10.1063/1.526150zbMath0551.76070OpenAlexW2081506421MaRDI QIDQ3343683

Louis Fishman, John J. McCoy

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1063/1.526150

zbMATH Keywords

square root operator(Schrödinger) equation(Weyl pseudodifferential) equationhalf-space propagatortransition from elliptic to parabolic wave theorytransversely inhomogeneous mediumunderlying stochastic process

Mathematics Subject Classification ID

Hydro- and aero-acoustics (76Q05) Applications of manifolds of mappings to the sciences (58D30)

Related Items (11)

Generalization of the Bremmer coupling series ⋮ Phase space methods and path integration: the analysis and computation of scalar wave equations ⋮ Pseudodifferential operators, operator orderings, marching algorithms and path integrals for one-way equations ⋮ Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile ⋮ Exact solutions of the Helmholtz-Weyl composition equation in underwater acoustics -- the quadratic profile ⋮ Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile ⋮ Exact and approximate solutions of the Helmholtz, Weyl composition equation in scalar wave propagation ⋮ Parabolic approximation of nonlocal boundary conditions for elastic seabeds ⋮ Generalization of the phase-screen approximation for the scattering of acoustic waves. ⋮ Reciprocity and representation theorems for flux- and field-normalised decomposed wave fields ⋮ Uniform high-frequency approximations of the square root Helmholtz operator symbol

Cites Work

• Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation
• A path-integral approach to the parabolic approximation. I
• On the WKB approximation to the propagator for arbitrary Hamiltonians
• The Feynman Integral
• Relation between the solutions of the Helmhotz and parabolic equations for sound propagation
• Hamiltonian Path-Integral Methods
• Quantum Operator Ordering and the Feynman Formulation

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