Momentum Probabilities for a Single Quantum Particle in Three-Dimensional Regular ‘Infinite’ Wells: One Way of Promoting Understanding of Probability Densities

Abstract

Students often wrestle unsuccessfully with the task of correctly calculating momentum probability densities and have difficulty in understanding their interpretation. In the case of a particle in an ‘infinite’ potential well, its momentum can take values that are not just those corresponding to the particle’s quantised energies but will be found to have values that occur with probabilities given by applying the Born Statistical Postulate. Momentum probability densities for several ‘infinite’ potential wells are plotted and some representative numerical values calculated and discussed. Students will benefit from these solutions, as they will aid their understanding of momentum space descriptions of quantum systems, momentum probability densities and their visualisation.