In the GRW spontaneous collapse model (for example) the wave-function evolves by linear Schrödinger equation, except, at random times, wave-function experiences a jump of the form:
\psi_t(x_1, x_2, ..., x_n) \rightarrow \frac{L_n(x)\psi_t(x_1, x_2, ..., x_n)}{||\psi_t(x_1, x_2, ..., x_n)||}...