  We clarify and study our previous observation that, under a compactification
with boundaries or orbifolding, vacuum expectation value of a bulk scalar field
can have different extra-dimensional wave-function profile from that of the
lowest Kaluza-Klein mode of its quantum fluctuation, under presence of
boundary-localized potentials which would be necessarily generated through
renormalization group running. For concreteness, we analyze the Universal Extra
Dimension model compactified on orbifold $S^1/Z_2$, with brane-localized Higgs
potentials at the orbifold fixed points. We compute the Kaluza-Klein expansion
of the Higgs and gauge bosons in an $R_\xi$-like gauge by treating the
brane-localized potential as a small perturbation. We also check that the
$\rho$ parameter is not altered by the brane localized potential.
