# Wave packet vs relative probability

1. Jan 20, 2007

### xboy

For a free particle,the one dimensional Schrodinger's equation gives a solution of the form Ae^i(kx - wt).This solution does not meet the normalisation requirement.According to Bransden-Joachain's texr,there are 2 ways out of this difficulty.One is to superpose and form localised wave packets.The other is to
"give up the concept of absolute probabilities when dealing with wave functions such as (above) which are not square integrable.Instead |psi(r,t)|^2dr is interpreted as the relative probability of finding the electron at time t in a volume element dr centred around r,so that the ratio |psi(r1,t)|^2 / |psi(r2,t)|^2 gives the probability of finding the particle within volume element centred around r=r1,compared with that of finding it within the same volume element at r=r2.For theparticular case of the plane wave we see that...there is equal chance of finding the particle at any point."

My question is,why do we prefer the first solution(wave packets) to the second one(relative probabilities)?