We now move to an alternative description of mixed quantum classical treatment of the dynamics known as Fewest Switches Surface Hopping (FSSH), which is one of many variants of the surface hopping. This method approaches the problem in a more classical way, propagating the nuclei on a single adiabatic surface until a discontinuous hop is performed. Once a hop is achieved, which must satisfy energy conservation through a rescaling of the classical nuclear velocities, then the nuclear forces are now derived from the new adiabatic state. The electronic DOFs are propagated according to the Schrodinger equation, and the probabilities for hopping between adiabatic states are proportional to the first-order non-adiabatic couplings d αβ between adiabatic states. This approach has also been recently used to simulate polariton chemistry. It is well-known that surface hopping approaches perform better when the propagation is done in the adiabatic (i.e., polariton) basis. However, many "tricks" exist to propagate the quantum mechanical DOFs in a locally diabatic basis for higher accuracy and to work around the sharply peaked non-adiabatic couplings throughout the nuclear dynamics. The total wavefunction for the quantum mechanical DOFs (i.e., the electrons and photons) can be written as,