Quantum corrections can be important for diffusion and the melting temperature of dense plasmas in compact astrophysical objects, particulary white dwarfs and neutron stars. Typically ions in these systems are modeled classically, but Daligault et al. use a semiclassical inter-ion potential. We run molecular dynamic simulations using this semiclassical approach in order to calculate the diffusion coefficient and melting temperatures in a one component plasma. We find that in liquid simulations quantum corrections do not have a significant effect on diffusion, increasing it by only a factor of two from our classical simulation. However, in solid simulations, diffusion slowly increases for small quantum corrections, but once quantum effects become large enough, the system can liquify. We also find that quantum corrections can decrease the melting temperature of a one component plasma, potentially affecting the way in which white dwarfs cool. These results suggest that a helium white dwarf may remain liquid at typical white dwarf densities, while the structure of a neutron star's crust could be altered due to quantum effects.