In quantum mechanics, the behavior of electrons (and other quantum particles) is described by wave functions, which can exhibit wave-like properties such as interference and diffraction. When the electron is considered as a wave, it doesn't mean that it is permanently in a wave state or that it can't return to a particle-like state. The wave-particle duality means that quantum objects can exhibit both wave-like and particle-like properties depending on the experimental setup and the measurement being performed.
When a measurement is made on a quantum system, the wave function collapses into one of the possible eigenstates corresponding to the observable being measured. This collapse can result in the electron being detected as a localized particle at a specific position. However, after the collapse, the wave function can evolve again and exhibit wave-like behavior until the next measurement is made.
The time evolution of the wave function is governed by the Schrödinger equation in quantum mechanics, which describes how the wave function changes over time. This evolution allows the wave function to propagate, interfere, and exhibit wave-like characteristics. However, when a measurement or interaction occurs, the wave function collapses, and the electron is observed as a particle at a particular location.
So, in summary, electrons (and other quantum particles) can exhibit both wave-like and particle-like behavior. The wave function describes their probabilistic behavior, and when a measurement is made, it can collapse into a localized state, after which it can evolve again as a wave until another measurement or interaction takes place. The specific conditions and experimental setups determine the probability of observing the electron as a wave or a particle.