Lindbald master equation is the equation that generalizes the Schrodinger equation.

The following is the equation written in terms of density matrix $\rho$

$$\frac{d\rho}{dt} = -\frac{i}{\hbar}[H, \rho] + \sum_k\left(L_k^\dagger L_k - \frac{1}{2}\{L_k^\dagger L_k, \rho\}\right)$$