  Very first time Elzaki transform is used in non relativistic quantum
mechanics to solve $N$-dimensional Schr\"{o}dinger equation in a closed form
for different solvable potential models. A universal transformation scheme is
introduced and a formula based approach is developed which shows how to apply
Elzaki transform to differential equation with non-constant coefficients that
generally appear in solving quantum mechanical initial value problems specially
for multidimensional Schr\"{o}dinger equation.
