Maxwell-Schrödinger Equation for X-Ray Laser Propagation andInterferometry Measurement of Plasma Electron Density

By starting with Maxwell theory of the x-ray laser propagation in collisionless plasmas, we study the phase difference of the probe beam and reference beam of x-ray laser interferometry in measuring the plasma electron density. The basic idea is to reduce the Maxwell equation to a Schroedinger-like equation. By using the quantum mechanical technique and introducing a novel picture, we obtain a modified relation between the phase and the electron density, where the phase corresponds to the interference of probe and reference light and the contribution of gradient of the electron density has been taken into account.