The temporal dynamics of the quantum Zakharov equations (QZEs) in one spatial dimension, which describes the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is revisited by considering their solution as a superposition of three interacting wave modes in Fourier space. Previous results in the literature are modified and rectified. Periodic, chaotic as well as hyperchaotic behaviors of the Fourier-mode amplitudes are identified by the analysis of Lyapunov exponent spectra and the power spectrum. The periodic route to chaos is explained through an one-parameter bifurcation analysis. The system is shown to be destabilized via a supercritical Hopf-bifurcation. The adiabatic limits of the fully spatio-temporal and reduced systems are compared from the viewpoint of integrability properties.