Generally, the adiabatic approximation is defined via a projection onto an adiabatically moving electronic base. The Hamiltonian then is separated into three constituents (lsquo;lsquo;adiabatic,rsquo;rsquo; lsquo;lsquo;diagonalhyphen;nonadiabatic,rsquo;rsquo; lsquo;lsquo;nondiagonalhyphen;nonadiabaticrsquo;rsquo;). A model system is considered for which the correct zerohyphen;order eigenfunctions are known. It is shown that with theseany singleof the three Hamiltonian constituents yieldsdiverging expectationvalues; only their sum yields convergence. From this the conclusion seems stringent that any result pertaining to electronic transitions, which is based on the adiabatic approximation, is an artifact.
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