Quantum Reports, Vol. 6, Pages 147-155: A Normalization Condition for the Probability Current in Some Remarkable Cases

Quantum Reports, Vol. 6, Pages 147-155: A Normalization Condition for the Probability Current in Some Remarkable Cases

Quantum Reports doi: 10.3390/quantum6020012

Authors: Antonio Feoli Elmo Benedetto Antonella Lucia Iannella

Starting from the dynamics of a bouncing ball in classical and quantum regime, we have suggested in a previous paper to add an arbitrary function of time to the standard expression of the probability current in quantum mechanics. In this paper, we suggest a way to determine this function: imposing a suitable normalization condition. The application of our proposal to the case of the harmonic oscillator is discussed.