  In this note, we discuss the quantum Hele-Shaw flow, a random measure process
in the complex plane introduced by the physicists P.Wiegmann, A. Zabrodin, et
al. This process arises in the theory of electronic droplets confined to a
plane under a strong magnetic field, as well as in the theory of random normal
matrices. We extend a result of Elbau and Felder to general external field
potentials, and also show that if the potential is $C^2$-smooth, then the
quantum Hele-Shaw flow converges, under appropriate scaling, to the classical
(weighted) Hele-Shaw flow, which can be modeled in terms of an obstacle
problem.
