A particle is confined to the one-dimensional space 0 ≤ x ≤ a , and classically it can be in any small interval dx with equal probability. However, quantum mechanics gives the result that the probability distribution is proportional to sin 2 ( nπ x/a ), where n is an integer. Find the variance in the particle's position in both the classical and quantum mechanical pictures, and show that, although they differ, the latter tends to the former in the limit of large n , in agreement with the correspondence principle of physics.