What is the wavefunction in quantum mechanics, and how does it relate to the behavior of electrons?

The wavefunction is a mathematical description of a particle’s quantum state, written as ψ(x,t), that encodes how the particle behaves like a wave. Its squared magnitude, |ψ|², gives the probability of finding the particle at a particular location, so it tells us where an electron is most likely to be seen. Because electrons act as both particles and waves, the wavefunction captures interference, tunneling, and energy quantization that govern their motion. For example, in a hydrogen atom the wavefunction for the 1s orbital is a smooth, bell‑shaped curve, and the peak of |ψ|² shows the electron is most likely near the nucleus. Thus, the wavefunction is the key link between the abstract math of quantum mechanics and the real, measurable behavior of electrons.