Integral formulation of the Ginzburg-Landau theory of the laser

The most probable laser mode amplitudes are calculated on the basis of the stationary momentum space solution of the Fokker-Planck equation for a continuum mode laser oscillator, which has been derived in a previous paper. Using Fourier transform techniques the expression is transformed from momentum space to configuration space, such that an integral equation results for the most probable field configuration. The kernel is calculated explicitly and the earlier presented Ginzburg-Landau equation for the laser field is recovered together with its boundary condition.