A possible solution to Einstein’s problem of 1953: the velocity of a quantum particle in a box

According to the prediction of the classical physics, a macroscopic body moves oscillating between two perfectly reflecting walls with a velocity proportional to its energy. On the contrary, the momentum of the body calculated in the framework of the de Broglie–Bohm interpretation of quantum mechanics is vanishing. This result was considered unsatisfactory by Einstein and other scientists who believed that also for quantum particles, it must be possible to move in an oscillatory way. In order to give an answer to Einstein’s objection, we show that it is possible to obtain a motion of the body using the standard rules of quantum mechanics. We obtain a correction of the Schrödinger equation, and we calculate explicitly the solution for the case of the particle in a box. Finally, we find the expression of the quantum velocity.