scholarly journals On the Born-Oppenheimer approximation of wave operators in molecular scattering theory

1993 ◽  
Vol 152 (1) ◽  
pp. 73-95 ◽  
Author(s):  
M. Klein ◽  
A. Martinez ◽  
X. P. Wang
Keyword(s):  
Scattering Theory ◽  
Molecular Scattering ◽  
Wave Operators ◽  
Oppenheimer Approximation

On the Born–Oppenheimer approximation of diatomic wave operators. II. Singular potentials

1997 ◽  
Vol 38 (3) ◽  
pp. 1373-1396 ◽  
Author(s):  
Markus Klein ◽  
André Martinez ◽  
Xue Ping Wang
Keyword(s):  
Singular Potentials ◽  
Wave Operators ◽  
Oppenheimer Approximation

Imbedded matrix Green’s functions in atomic and molecular scattering theory

1983 ◽  
Vol 78 (7) ◽  
pp. 4456-4463 ◽  
Author(s):  
J. V. Lill ◽  
T. G. Schmalz ◽  
J. C. Light
Keyword(s):  
Scattering Theory ◽  
Green's Functions ◽  
Green’S Functions ◽  
Molecular Scattering

scholarly journals WAVE PROPAGATION AND SCATTERING FOR THE RS2 BRANE COSMOLOGY MODEL

2009 ◽  
Vol 06 (04) ◽  
pp. 809-861 ◽  
Author(s):  
ALAIN BACHELOT
Keyword(s):  
Cauchy Problem ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Asymptotic Completeness ◽  
Decay Estimates ◽  
Brane Cosmology ◽  
Dispersive Waves ◽  
Wave Operators ◽  
Global Cauchy Problem

We study the wave equation for the gravitational fluctuations in the Randall–Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L1-L∞, L2-L∞ decay estimates and global Lp Strichartz type inequalities. We develop the complete scattering theory: existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.

scholarly journals SPECTRAL ANALYSIS AND TIME-DEPENDENT SCATTERING THEORY ON MANIFOLDS WITH ASYMPTOTICALLY CYLINDRICAL ENDS

2013 ◽  
Vol 25 (02) ◽  
pp. 1350003 ◽  
Author(s):  
S. RICHARD ◽  
R. TIEDRA DE ALDECOA
Keyword(s):  
Spectral Analysis ◽  
Time Delay ◽  
Hilbert Spaces ◽  
Scattering Theory ◽  
Asymptotic Completeness ◽  
Time Dependent ◽  
Resolvent Estimates ◽  
Wave Operators ◽  
Use Of Time ◽  
Stationary Scattering

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud–Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.

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