A simplifying assumption called the Born approximation rests on the largeness of the bath and the relative weakness of the coupling, which is to say the coupling of the system to the bath should not significantly alter the bath eigenstates.
22.
Generally in scattering theory and in particular in quantum mechanics, the "'Born approximation "'consists of taking the incident field in place of the total field as the driving field at each point in the scatterer.
23.
In the continuum limit, this becomes an integral over the density \ rho ~, and if the deflection is small we can approximate the gravitational potential along the deflected trajectory by the potential along the undeflected trajectory, as in the Born approximation in quantum mechanics.
24.
The "'Cauchy Born rule "'or "'Cauchy-Born approximation "'is a basic hypothesis used in the mathematical formulation of solid mechanics which relates the movement of atoms in a crystal to the overall deformation of the bulk solid.
25.
In these simple cases, no automatic packages are needed and cross-section analytical expression can be easily derived at least for the lowest approximation : the Born approximation also called the leading order or the tree level ( as Feynman diagrams have only trunk and branches, no loops ).
