  The effect of an externally applied high frequency oscillating electric field
on the critical nucleation field of superconductivity in the bulk as well as at
the surface of a superconductor is investigated in details in this work.
Starting from the linearized time dependent Ginzburg-Landau (TDLG) theory and
using the variational principle we have shown the analogy between a quantum
harmonic oscillator with that of the nucleation of superconductivity in bulk
and a quantum double oscillator with that of the nucleation at the surface of a
finite sample. The effective Hamiltonian approach of Cook {\it et al}
\cite{cook} is employed to incorporate the effect of an externally applied
highly oscillating electric field. The critical nucleation field ratio is also
calculated from the ground state energy method. The results obtained from these
two approximated theories agree very well with the exact results for the case
of undriven system which establishes the validity of these two approximated
theories. It is observed that the highly oscillating electric field actually
increases the bulk critical nucleation field ($H_{c_2}$) as well as the surface
critical nucleation field ($H_{c_3}$) of superconductivity as compared to the
case of absence of electric field ($\varepsilon_0=0$). But the externally
applied rapidly oscillating electric field accentuates the surface critical
nucleation field more than the bulk critical nucleation field i.e. the increase
of $H_{c_3}$ is 1.6592 times larger than that of $H_{c_2}$.
