Wave Function Collapse During Reactions When a proton and electron combine to form Hydrogen gas after the big bang, would the wave function of the electron collapse as they bond together?
 A: First of all, the electron and proton have to be described by a joint wave function, $\Psi(\mathbf{r}_p, \mathbf{r}_e)$. In many QM books one often treats the Hydrogen atom, as if it was a problem of an electron in a static Coulomb field. The correct approach is to start with the Schrödinger equation for the two particles and then perform transformation to the center-of-mass reference frame. While this works when calculating the energy levels of an isolated atom, it is a bad approach, if we want to consider collision, where both particles will interact with their environment.
If we treat this as a scattering problem, we can start with two plane waves, which means that the energy of the system "proton+electron" is positive and they are not bound (or the binding energy is extremely small). The bound state will occur after the system loses some energy due to interactions with its environment, e.g., via emitting a photon or scattering with other particles. The environment in this case would play a role of a microscopic project with infinite degrees of freedom, triggering the wave function collapse (note thatt we still talk about the joint function of the two particles).
Remark: I admit that the discussion above is general, i.e. it does not account for the specific conditions that might have existed after the Big Bang.
A: There is a wave associated with each sub-atomic “particle”.  The properties of the wave determine the probability that the particle will interact with something else at a given point. A “wave function” can be used to model the properties of the wave. After an interaction, the properties of the wave change and you need a new function.
