Adiabatic and diabatic representations, coordinate and unitary transformations: coupled oscillators

Abstract

The relationships between the adiabatic approximation and a transformation of the coordinates or the Hamiltonian are investigated for a two-dimensional coupled oscillator. The Smith transformation is used systematically to obtain a transformation returning the adiabatic form of the Hamiltonian to its original ‘diabatic’ form and thus provides a method of obtaining the unitary transformation that is equivalent to the coordinate transformation.