Yes, in quantum mechanics, the wave function of one particle can indeed affect the wave function of another particle, a phenomenon known as quantum entanglement or quantum correlation. This concept is a fundamental aspect of quantum theory and is responsible for non-local, instantaneous correlations between particles.
When two or more particles become entangled, their wave functions become intertwined and cannot be described independently of each other. This means that the state of one particle cannot be fully described without considering the state of the other particle(s).
The specific nature of the entanglement depends on the initial conditions and the interactions between the particles. For example, if particles 1 and 2 become entangled, measurements made on particle 1 can instantaneously influence the state of particle 2, regardless of the distance between them. This instantaneous correlation is often referred to as "spooky action at a distance."
It's important to note that the wave function describes the probability distribution of possible outcomes for a particle's properties when measured. The actual outcome of a measurement is determined upon measurement, and it may collapse the wave function of the particle being measured and also instantaneously affect the wave function of the entangled particle(s).
Quantum entanglement has been experimentally confirmed through numerous tests, including the famous Bell's theorem experiments, which have shown that the correlations between entangled particles violate classical concepts such as local realism.
The phenomenon of quantum entanglement is an active area of research and has applications in various fields, including quantum computing, quantum cryptography, and quantum communication.