TY - JOUR
T1 - Perturbation theory and the two-level approximation
T2 - A corollary and critique
AU - Andrews, David L.
AU - Bradshaw, David S.
AU - Coles, Matt M.
PY - 2011/2/8
Y1 - 2011/2/8
N2 - This analysis addresses the use of a two-level approximation to simplify expressions derived from perturbation theory. It is shown that the limitations of validity for the emergent results are more stringent than is commonly understood, being equivalent in effect to the adoption of a more extensive approximation - one that significantly undermines the perturbative origin of those expressions. Effectively truncating the completeness relation, a series of interconnected operator relations comes into play, some with physically untenable consequences. A new theorem on the expectation values of operator functions highlights additional constraints upon any molecule modelled as a two-level system. © 2010 Elsevier B.V. All rights reserved.
AB - This analysis addresses the use of a two-level approximation to simplify expressions derived from perturbation theory. It is shown that the limitations of validity for the emergent results are more stringent than is commonly understood, being equivalent in effect to the adoption of a more extensive approximation - one that significantly undermines the perturbative origin of those expressions. Effectively truncating the completeness relation, a series of interconnected operator relations comes into play, some with physically untenable consequences. A new theorem on the expectation values of operator functions highlights additional constraints upon any molecule modelled as a two-level system. © 2010 Elsevier B.V. All rights reserved.
UR - http://www.scopus.com/inward/record.url?scp=79751523880&partnerID=8YFLogxK
U2 - 10.1016/j.cplett.2010.12.055
DO - 10.1016/j.cplett.2010.12.055
M3 - Article
VL - 503
SP - 153
EP - 156
JO - Chemical Physics Letters
JF - Chemical Physics Letters
SN - 0009-2614
IS - 1-3
ER -