Question

why is normalisation necessary in a wave function

Answer 1

If we take product of wave function with its complex conjugate we get the probability density. Now if we want to find a probability of finding a partilce in given interval then we have to integrate the probability density over that interval.

If we integrate probability density over entire space i.e. from plus infinity to minus infinity we should get answers as 1. Because total probability is always equal to one also you are integrating over entire space so you will surely find particle somewhere, hence total probability is one.

But if you use the wave function which is not normalized for finding the probability over entire space you don't get the total probability equal to one. Hence inorder to get total probability as one we need to normalize the wave function.