what is wave function
An atomic orbital is represented by the wave function ψ, for an electron in an atom, and is associated with a certain amount of energy. There can be many orbitals in an atom, but an orbital cannot contain more than two electrons. The orbital wave function ψ gives all the information about an electron. And the square of wave function, |ψ|2is known as probability density, and from its value at different points within an atom, the probable region for finding an electron around the nucleus can be predicted.
In the physical sense, ψ gives the amplitude of the wave associated with the electron. It is known that in case of light waves, the square of the amplitude of the wave at a point is proportional to the intensity of light. Extending the same concept to electron wave motion, the square of the wave function, |ψ|2 may be taken as intensity of electron at any point. In other words, |ψ|2 gives the probability density. Thus, |ψ|2 has been called the probability density and ψ the probability amplitude.