  The present work focuses on the calculation of a non-adiabatic transition
probability between two states which may or may not cross with each other and
are coupled to each other by a moving $\delta$ function potential. Here, the
time dependent Schrodinger equation is converted to time independent one by
using a scaling factor which is function of time. This time independent
Schrodinger equation is then considered for two potentials coupled by a moving
$\delta$ potential and an expression for non-adiabatic transition probability
has been derived.
