Question

what is wave function?
Simple definition of wave function?

Answer 1

A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves.

Answer 2

each particle is represented by wave function|:1337593471544:(position,time) such as that

Answer 3

The wave function describes where the participle can exist over time

Answer 4

A wavefunction is a complex function of space and time coordinates (e.g. W = W(x,y,z,t)) the amplitude squared of which (i.e. W*W, where W* is the complex conjugate of W) tells you the probability density of finding a particle at a given location at a given time.

It is a way to incorporate two "wavelike" phenomena into the classical description of the motion of a particle: (1) quantization of energy in bound states, and (2) interference, e.g. as you find in the double-slit experiment. Both of these things fall out naturally from any description of mechanics that uses waves.

The tricky bit is that aside from the phenomena above, we do not see particles like electrons and atoms behaving as waves, so you have to wave your hands a little and talk about exactly how to interpret the wavefunction, so that you end up with a particle that has these wavelike properties. This tends to get confusing. It may be best to regard the wavefunction as just a tool, a mathematical widget that lets you predict the right properties about a particle. (It is possible to do quantum mechanics without waves, but it tends to get a little abstract. I think the idea is that undergraduates are likely to be familiar with waves from basic physics classes.)