In quantum mechanics, the wave function of a particle represents the probability distribution of finding the particle in different states. It is a mathematical function that evolves over time according to the Schrödinger equation.
The initial state of the wave function, often referred to as the "wave function at t=0," is typically specified based on the experimental setup or the preparation procedure of the system. The specific choice of the initial state depends on the context of the experiment or the problem being analyzed.
The wave function does not directly encode information about the particle's previous measurement or its last location. Instead, it describes the probabilities of finding the particle in different locations or states when a measurement is made. When a measurement is performed on the particle, the wave function "collapses" into one of the possible measurement outcomes, and the particle is found in a specific state or location.
It's important to note that the interpretation of the wave function and the process of measurement in quantum mechanics are subjects of ongoing debate and different interpretations exist. The collapse of the wave function is one interpretation, often associated with the Copenhagen interpretation, but other interpretations, such as the many-worlds interpretation or the pilot-wave theory, propose alternative explanations for the measurement process.
In summary, the wave function of a particle is not centered on the particle's last measured location but describes the probabilities of finding the particle in different states or locations when a measurement is made.