The wave function of a particle is not centered on any specific location in physical space. Instead, it describes the probability distribution of finding the particle in different locations when a measurement is made.
According to quantum mechanics, the wave function of a particle evolves over time according to the Schrödinger equation. This evolution is determined by the initial conditions of the wave function and the physical laws governing the system. The wave function encodes information about the particle's possible states and the probabilities of measuring certain values, such as position or momentum, when a measurement is performed.
When a measurement is made on a quantum system, the wave function collapses or "reduces" to one of the possible eigenstates associated with the measured observable. The specific outcome of the measurement is probabilistic, and the probability of obtaining a particular result is given by the square of the corresponding coefficient in the wave function expansion.
The location of the last measurement does not directly determine the center of the wave function for subsequent measurements. The wave function evolves in a way that allows the particle to exist in a superposition of states, and subsequent measurements may yield different outcomes based on the probabilistic nature of quantum mechanics.
It is worth noting that interpretations of quantum mechanics, such as the Copenhagen interpretation or the many-worlds interpretation, provide different perspectives on the nature of the wave function and its relation to measurements. These interpretations offer different explanations for how and why measurements yield specific outcomes, but the underlying probabilistic nature of quantum mechanics remains a fundamental aspect of the theory.