According to the principles of wave-particle duality in quantum mechanics, the wave function of a particle does indeed imply that the particle can exist in multiple locations simultaneously. However, it's important to understand that the wave function represents the probability distribution of finding the particle in different positions rather than its actual physical presence in all those locations at once.
The wave function describes the state of a particle and provides information about the likelihood of finding it in a particular location when a measurement is made. This probability distribution can be spread out over space, meaning that there is a finite chance of finding the particle in various regions.
However, when a measurement is made to determine the particle's position, the wave function "collapses" to a specific value, and the particle is found at a particular location. This is often referred to as the "collapse of the wave function" or "wave function collapse."
Regarding your question about whether an electron can potentially exist anywhere in the whole universe and interact with any other particle, the answer is both yes and no. In theory, the wave function allows for the possibility of an electron to be found anywhere in the universe, although the probability of finding it in extremely distant locations becomes exceedingly low. However, the likelihood of interactions between particles decreases significantly as the distance between them increases.
Furthermore, the wave function is influenced by various factors, such as potential barriers, forces, and interactions with other particles. These factors can affect the behavior of the wave function and restrict the regions where the particle is more likely to be found.
In summary, while the wave function allows for the possibility of a particle like an electron to exist in multiple locations simultaneously, the actual measurement of its position will yield a specific result. The likelihood of finding a particle in distant regions of the universe becomes highly improbable, and the interactions between particles decrease significantly with increasing distances.