Equivalent Hamiltonian of an Electron Gas at High Density

Recently Wentzel presented a method of the equivalent Hamiltonian of an electron gas based on Sawada's theory. In this theory the Bloch interaction has been adopted as the interaction between electrons and phonons together with the mutual Coulomb interaction with electrons in the explicit form. If the Bloch interaction is assumed, the mutual interaction of electrons should be of a screened form. If the mutual interaction is assumed in the explicit Coulombic form, the attractive Coulomb potential should be adopted as the interaction between electrons and ions in place of the Bloch interaction. Some modification becomes necessary to derive physically meaningful results. Wentzel's equivalent Hamiltonian is very similar to the Hamiltonian of coupled oscillators previously proposed. Both for an electron gas and for an electron-pion plasma it can be shown that results derived from the one are in fair agreement with those from the other.