No, a particle cannot have a wave function without being in a state of superposition. The wave function describes the quantum state of a particle and contains information about the probability distribution of the particle's properties, such as position or momentum.
In quantum mechanics, superposition refers to the ability of a quantum system to exist in multiple states simultaneously. This means that the wave function of the system is a combination, or superposition, of different possible states. These superposed states interfere with each other, leading to characteristic wave-like behavior.
If a particle is in a state of superposition, its wave function is a linear combination of multiple states, each with an associated probability amplitude. This allows the particle to exhibit interference effects and possess properties that are not confined to a single value.
On the other hand, if a particle is not in a state of superposition, its wave function collapses to a single state or eigenstate. The particle's properties become definite and well-defined, rather than being spread out in a probability distribution. In this case, the wave function no longer exhibits the wave-like behavior associated with superposition.
Therefore, having a wave function implies the possibility of superposition, while a particle in a definite state would not exhibit a wave function.