Numeric Solution to Master Equations of Lasers and Condensation N Bosons

We solve master equations for the diagonal terms of a density matrix for a one mode laser state or condensation N Bosons state with the following form

$$ \dot{p_m} = - G_m * (m+1) * p_m + G_{m-1} * m * p_{m-1} - L_m * m * p_m + L_{m+1} * (m+1) * p_{m+1} $$