  A novel and readily understandable derivation of the Golden Rule of time
dependent perturbation theory is presented. The derivation is based on
adiabatic turning on of the perturbation as used, for instance, in some formal
developments of scattering theory. Energy conservation is expressed in terms of
an intuitively and physically appealing Lorentzian line shape rather than the
artificial, oscillatory sin(x)=x type line shape that appears in conventional
derivations. The conditions for the derivation's validity are compactly and
conveniently expressed in the frequency/energy domain rather than in the usual
time domain. The derivation also highlights how, along with energy
conservation, the transition rate faithfully and instantaneously follows the
variations in the square of the perturbing potential as one may expect in the
adiabatic limit. In the first instance, the adiabatic turning on is achieved,
as usual, by a single exponential time variation. But we demonstrate that the
instantaneous following of the square of the perturbing potential by the
transition rate is more general and that one can derive the Golden Rule for a
general slowly varying time dependent perturbation. This allows one to derive
generalisations of the simple decay law, originally derived in the classic
paper by Weisskopf and Wigner; a tutorial exposition of the essence of this
classic work is provided. The Oppenheimer method for applying the Golden rule
to problems, such as the electric field ionisation of atoms, in which the
perturbing potential can also create the final states, is reviewed. No use of
an energy gap condition is needed to derive our results on adiabatic behaviour
in contrast to the origianl derivations of the adiabatic theorem in quantum
mechanics.
