Question

A particle is confined to the one-dimensional space 0 sx s 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 (mTx/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.

Answer 1