The quantum oscillation in a one-dimensional ring with two leads is in
vestigated with magnetic flux and electrostatic potential applied simu
ltaneously. A transmission coefficient is derived for various conditio
ns. The amplitude and frequency of the conductance oscillation in a me
soscopic ring as a function of either potential are modulated by holdi
ng the other constant. At a certain electrostatic potential and Fermi
energy, h/2e oscillations are correctly predicted for the magnetostati
c Aharonov-Bohm effect. A similar half-periodic oscillation occurs in
the electrostatic case at a certain magnetic flux. A theory is formula
ted from our earlier numerical calculations and phenomenological inter
pretations, based on an analytical expression, for a fuller understand
ing of the origin and mechanism of this behavior. We also investigate
the influence of scattering at the junctions on the quantum oscillatio
n.