  Recent more precise experiments have revealed both a slow and a fast quantum
oscillation in the c-axis resistivity of nearly optimal to overdoped
electron-doped high temperature superconductor
$\mathrm{Nd_{2-x}Ce_{x}CuO_{4}}$. Here we study this problem from the
perspective of Fermi surface reconstruction using an exact transfer matrix
method and the Pichard-Landauer formula. In this method, neither quasiclassical
approximations for magnetic breakdown, nor {\em ad ho}c broadening of Landau
levels, are necessary to study the high field quantum oscillations. The
underlying Hamiltonian is a mean field Hamiltonian that incorporates a two-fold
commensurate Fermi surface reconsruction. While the specific mean field
considered is the $d$-density wave, similar results can also be obtained by a
model of a spin density wave, as was explicitly demonstrated earlier. The
results are consistent with an interplay of magnetic breakdown across small
gaps in the reconstructed Fermi surface and Shubnikov-de Haas oscillations.
