"INVARIANT IMBEDDING" AND WAVE PROPAGATION IN INHOMOGENEOUS MEDIA

Technical Report · Wed Nov 01 04:00:00 EST 1961

OSTI ID:4802186

MacCallum, C J

The study of wave propagation in one dimensional inhomogeneous niedia is undertaken using thie mathematical approach recently developed under the name invariant imbedding.'' The specific problem posed is to find the transmission and reflection amplitudes for waves incident on an inhomogeneous transition region'' separating two homogeneous media. By imbedding'' the actual problem into a continuum of problems generated by a real parameter, first-order nonlinear differential equations for the amplitudes are constructed; these contain an arbitrary function to be chosen appropriate to the physical situation. Integral equations are constructed which yield very powerful approximations; in particular, improvements over the Born and WKB approximations are discussed. The Bremmer-Glauber series is rederived. Applications discussed include reflection of microwaves from a plasma boundary, reflection of elastic or electromagnetic waves obliquely incident on a stratified medium, determination of phase shifts in a partial wave analysis of spherical scattering, and determination of quantum mechanical energy levels in one dimension. (auth)

• Research Organization: Sandia Corp., Albuquerque, N. Mex.
• DOE Contract Number: AT(29-1)-789
• NSA Number: NSA-16-010676
• OSTI ID: 4802186
• Report Number(s): SC-4669(RR)
• Country of Publication: United States
• Language: English

Related Subjects

BORN APPROXIMATION
DIFFERENTIAL EQUATIONS
ELASTICITY
ELECTROMAGNETIC WAVES
ENERGY LEVELS
INTEGRAL EQUATIONS
INTEGRALS
INTERACTIONS
MICROWAVES
MOTION
PERTURBATION THEORY
PHASE SHIFT
PHYSICS
PLASMA
QUANTUM MECHANICS
REFLECTION
SCATTERING
SPECTRAL SHIFT
SURFACES
WAVE PROPAGATION
WKB APPROXIMATION