According to the principles of quantum mechanics, the wave function of a particle can exhibit a state of superposition, where it can be in multiple states simultaneously. However, it's important to clarify what is meant by "there" and "not there" in this context.
The wave function of a particle describes its quantum state and encompasses all the possible states the particle can occupy. It is a mathematical function that evolves over time, and its absolute square gives the probability distribution of finding the particle in different states when measured.
In the phenomenon of superposition, the wave function can be a combination of multiple states at the same time. This means that the particle can exist in a superposition of being "here" and "there" simultaneously, or in multiple states with different positions, velocities, or other properties. It's important to note that this superposition does not imply that the particle is physically present in two distinct locations simultaneously. Instead, it represents the range of possibilities for the particle's properties before a measurement is made.
When a measurement is performed on a particle in a superposition state, it "collapses" into one of the possible states, corresponding to the outcome of the measurement. This collapse is a probabilistic process, and the resulting state after measurement becomes definite and localized.
In summary, the wave function of a particle can exist in a superposition of states, allowing for the particle to be described by a combination of possibilities. However, upon measurement, the wave function collapses, and the particle is observed to be in a specific state, not in multiple states simultaneously.