wave represent the propagation of distabance in space. every wave is characterised by some quantity known as the wave variable which varies with spase and time. eg. the sound waves have pressure as the wave variable which varies with space and time, the light waves on strings have displacement y as the wave variable, the light waves that are electromagnetic, have the field variation.

The wave variable associated with the matter waves is called the wave function y and it mathematically describes the motion of an electron.

Physical Significance

Normalised Conditions

i) Ψ should be normalized wave function. ii) Ψ should be a single valued function of space and time (as the probability can have only one value at a given point.) iii) Ψ must be finite. (As infinite probability is meaningless) iv) The wave function ψ and its space derivatives ∂ψ/∂x, ∂ψ/∂y and ∂ψ/∂z must be continuous everywhere in the region where ψ is defined. A wave function satisfying all the above conditions is called a well-behaved function. Or The wave function which is finite, continuous and single valued is called as well behaved function.