 
Summary: Timeenergy coherent states and adiabatic scattering
J. E. Avrona)
Department of Physics, Technion, 32000 Haifa, Israel
A. Elgartb)
Jadwin Hall, Princeton University, Princeton, New Jersey 08544
G. M. Grafc)
Theoretische Physik, ETHHo¨nggerberg, 8093 Zu¨rich, Switzerland
L. Sadund)
Department of Mathematics, University of Texas, Austin, Texas 78712
Received 14 February 2002; accepted for publication 1 March 2002
Coherent states in the timeenergy plane provide a natural basis to study adiabatic
scattering. We relate the diagonal matrix elements of the scattering matrix in this
basis with the frozen onshell scattering data. We describe an exactly solvable
model, and show that the error in the frozen data cannot be estimated by the Wigner
time delay alone. We introduce the notion of energy shift, a conjugate of Wigner
time delay, and show that for incoming state (H0) the energy shift determines the
outgoing state. © 2002 American Institute of Physics. DOI: 10.1063/1.1476952
I. INTRODUCTION
Scattering from a slowly changing scatterer is described, to leading order, by a time indepen
dent scatterer frozen at the scattering time.1
