Quantum formulation of plasma physics

I formulate plasma physics according to postulates of quantum mechanics, base on electron number density. List of Plasma Quantity: $n_e=\frac{dN}{dV}$ electron number density. $j=n_e.u$ electron number current density where the $u$ denotes velocity. $H_v=\frac {j^2}{2n_e}+U_v=E_v$ This is Number Hamiltonian density where the $U_v$ denotes Number potential energy density and $E_v$ denotes Number total energy density. $R_m$ Magnetic Reynolds Number. $k_m=\frac {R_m}{L}$ Magnetic reynolds wave number. $\psi_m$ magnetic wave function. $\zeta=n_e.\eta$ dynamic magnetic diffusivity where the $\eta$ denotes magnetic diffusivity. Essential Relations: $j=\zeta .k_m=n_e.u$ and then, $\nabla^2\psi_m+k_m^2\psi_m=0$ where the $\nabla^2$ is laplacian operator. $\frac {-\zeta^2\nabla^2\psi_m}{(1+\gamma)n_e}+U_v\psi_m=E_v\psi_m$ this is my equation of plasma that appears to be an relativistic expression of schrodinger equation, where the $\gamma$ denotes lorentz factor and at low speeds $\gamma+1=2$ and so on...etc.