Abstract
In this work, using recently obtained expansion of the dielectric function in the long wave length limit by Moldabekov et al (2015 Phys. Plasmas 22 102104), we extended previously obtained formulas for the equation of state of the semiclassical dense plasma from Ramazanov et al (2015 Phys. Rev. E 92 023104) to the quantum case. Inner energy and contribution to the pressure due to plasma non-ideality derived for both Coulomb pair interaction and quantum pair interaction potentials. Obtained analytical result for the equation of state reproduces the Montroll-Ward contribution, which corresponds to the quantum ring sum. It was shown that the obtained results are consistent with the Thomas-Fermi approximation with the first order gradient correction. Additionally, the generalization of the quantum Deutsch potential to the case of the degenerate electrons is discussed. Obtained results will be useful for understanding of the physics of dense plasmas as well as for further development of the dense plasma simulation on the basis of the quantum potentials.