scholarly journals Time delay is a common feature of quantum scattering theory

2012 ◽  
Vol 387 (2) ◽  
pp. 618-630 ◽  
Author(s):  
S. Richard ◽  
R. Tiedra de Aldecoa
Keyword(s):  
Time Delay ◽  
Scattering Theory ◽  
Quantum Scattering ◽  
Quantum Scattering Theory

scholarly journals TIME DELAY FOR DISPERSIVE SYSTEMS IN QUANTUM SCATTERING THEORY

2009 ◽  
Vol 21 (05) ◽  
pp. 675-708 ◽  
Author(s):  
RAFAEL TIEDRA DE ALDECOA
Keyword(s):  
Time Delay ◽  
Scattering Theory ◽  
Integral Formula ◽  
Radial Component ◽  
Quantum Scattering ◽  
Scattering Operator ◽  
Localization Operators ◽  
Quantum Scattering Theory ◽  
One Dimensional ◽  
Klein Gordon

We consider time delay and symmetrized time delay (defined in terms of sojourn times) for quantum scattering pairs {H0 = h(P), H}, where h(P) is a dispersive operator of hypoelliptic-type. For instance, h(P) can be one of the usual elliptic operators such as the Schrödinger operator h(P) = P2 or the square-root Klein–Gordon operator [Formula: see text]. We show under general conditions that the symmetrized time delay exists for all smooth even localization functions. It is equal to the Eisenbud–Wigner time delay plus a contribution due to the non-radial component of the localization function. If the scattering operator S commutes with some function of the velocity operator ∇h(P), then the time delay also exists and is equal to the symmetrized time delay. As an illustration of our results, we consider the case of a one-dimensional Friedrichs Hamiltonian perturbed by a finite rank potential. Our study puts into evidence an integral formula relating the operator of differentiation with respect to the kinetic energy h(P) to the time evolution of localization operators.

On the inverse problem in quantum scattering theory

2009 ◽  
Vol 28 (S19) ◽  
pp. 457-466
Author(s):  
Erkki Brändas ◽  
Erik Engdahl ◽  
Magnus Rittby ◽  
Nils Elander
Keyword(s):  
Inverse Problem ◽  
Scattering Theory ◽  
Quantum Scattering ◽  
Quantum Scattering Theory

Comparison of transition state theory with quantum scattering theory for the reaction Li+HF→LiF+H

1994 ◽  
Vol 100 (7) ◽  
pp. 4917-4924 ◽  
Author(s):  
C.‐Y. Yang ◽  
S. J. Klippenstein ◽  
J. D. Kress ◽  
R. T Pack ◽  
G. A. Parker ◽  
...  
Keyword(s):  
Transition State ◽  
Scattering Theory ◽  
Transition State Theory ◽  
State Theory ◽  
Quantum Scattering ◽  
Quantum Scattering Theory
Sign in / Sign up

Export Citation Format

Share Document