Let $S$ be a quantum system and let $D$ be a detector. Suppose that $D+S$ does not interact with the environment. Now when $D$ makes a measurement of $S$, the wave function of $S$ collapses. Therefore, the wave function of $S$ does not follow a unitary evolution, so it follows that it does not satisfy the Schrödinger equation during the measurement process.
But the combined system $D+S$ also has a wavefunction. On the one hand, you could argue that the wavefunction of $S$ is a part of this system, so since this wavefunction collapses, the wavefunction of $D+S$ can not satisfy the Schrödinger equation during the measurement process. On the other hand, $D+S$ is a closed system so it should satisfy the Schrödinger equation. How can this be resolved?
