Global Minimum Principle for Schr{umlt o}dinger Equation Inverse Scattering

Journal Article · Thu Oct 31 23:00:00 EST 1996 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.77.4126· OSTI ID:397640

Rose, J H ^[1]

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1. Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States)

A global minimum principle is reported for inverse scattering for Schr{umlt o}dinger{close_quote}s equation without bound states. For the one-dimensional problem, the line integral of the potential on the interval {l_brace}{minus}{infinity},{ital x}{r_brace} can be found by minimizing a certain functional of the scattering amplitude and a variational wave field. In three dimensions, the minimum of a closely related functional is shown to yield {minus}{integral}{ital d}{sup 3}y{nu}(y)/{vert_bar}x{minus}y{vert_bar}{sup 2}, where {nu}(x) is the potential. {copyright} {ital 1996 The American Physical Society.}

• Research Organization: Ames National Laboratory
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 397640
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 20 Vol. 77; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUND STATE
BOUND STATES
INVERSE SCATTERING PROBLEM
ONE-DIMENSIONAL CALCULATIONS
POTENTIALS
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS