Intense Field Molecular Photodissociation:
The Adiabatic Views
R. Lefebvre
Abstract The adiabatic theory requires the time scale of the changes in the
Hamiltonian to be larger than the time scale of the changes in the system. The
solution of the wave equation is expressed in terms of the instantaneous solutions.
A formalism known as the adiabatic Floquet theory is being currently applied to
describe photodissociation of molecules at high intensity in the optical range, where
these conditions are not fufilled. We show how to justify this approach, and we use
the direct solution of the time-dependent Schrodinger equation to confirm its
validity.
Keywords Molecular photodissociation Á Adiabatic theory Á Floquet formalism
1 Introduction
The adiabatic approach to treat a quantum system is considered as a useful tool
which avoids the difficult task of looking for the exact solutions of the timedependent Schrödinger equation [1–3]. The applicability of the method requires the
time scale for the variation of the time-dependent contribution to the Hamiltonian to
be larger than the time scale of the exposed system, given typically by the inverse of
level separations. The method, first developed for Hermitian Hamiltonian, has also
been applied to the dissipative case, that is to non-Hermitian Hamiltonians [4–6],
with also some discussion for the conditions of applicability [5]. We wish, in this
paper, to consider the case of a molecule exposed to a strong laser pulse. This
problem has sometimes been treated by the method called the adiabatic Floquet
R. Lefebvre (&)
Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS and UMR8214, Bât. 350,
Université Paris-Sud, F91405 Orsay, France
e-mail: roland.lefebvre@u-psud.fr
R. Lefebvre
U.F.R. de Physique Fondamentale et Appliquée, Université Pierre et Marie Curie,
75321 Paris, France
© Springer International Publishing Switzerland 2015
M.A.C. Nascimento et al. (eds.), Frontiers in Quantum Methods and Applications
in Chemistry and Physics, Progress in Theoretical Chemistry and Physics 29,
DOI 10.1007/978-3-319-14397-2_8
135
The Adiabatic Views
R. Lefebvre
Abstract The adiabatic theory requires the time scale of the changes in the
Hamiltonian to be larger than the time scale of the changes in the system. The
solution of the wave equation is expressed in terms of the instantaneous solutions.
A formalism known as the adiabatic Floquet theory is being currently applied to
describe photodissociation of molecules at high intensity in the optical range, where
these conditions are not fufilled. We show how to justify this approach, and we use
the direct solution of the time-dependent Schrodinger equation to confirm its
validity.
Keywords Molecular photodissociation Á Adiabatic theory Á Floquet formalism
1 Introduction
The adiabatic approach to treat a quantum system is considered as a useful tool
which avoids the difficult task of looking for the exact solutions of the timedependent Schrödinger equation [1–3]. The applicability of the method requires the
time scale for the variation of the time-dependent contribution to the Hamiltonian to
be larger than the time scale of the exposed system, given typically by the inverse of
level separations. The method, first developed for Hermitian Hamiltonian, has also
been applied to the dissipative case, that is to non-Hermitian Hamiltonians [4–6],
with also some discussion for the conditions of applicability [5]. We wish, in this
paper, to consider the case of a molecule exposed to a strong laser pulse. This
problem has sometimes been treated by the method called the adiabatic Floquet
R. Lefebvre (&)
Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS and UMR8214, Bât. 350,
Université Paris-Sud, F91405 Orsay, France
e-mail: roland.lefebvre@u-psud.fr
R. Lefebvre
U.F.R. de Physique Fondamentale et Appliquée, Université Pierre et Marie Curie,
75321 Paris, France
© Springer International Publishing Switzerland 2015
M.A.C. Nascimento et al. (eds.), Frontiers in Quantum Methods and Applications
in Chemistry and Physics, Progress in Theoretical Chemistry and Physics 29,
DOI 10.1007/978-3-319-14397-2_8
135