The techniques of wide-band and narrow-band approximations, which have been used in solid state theory, are applied to the theory of donor-bridge-acceptor models which are commonly used to represent molecular switches or wires. The approximations lead to analytical solutions which closely match the numerical calculations. These approximations are based on one of the simplest one-electron models where the interaction is time independent and the bridge band is completely initially empty. The form of the analytical solutions and the stability of the numerical calculations are discussed.