The quantum aspects of the Joule-Lenz law for the dissipation of energy imply for small transition energies the validity of the formula ∆E ∆t = h where ∆t is the transition time of an electron particle. The present paper points out that a similar relation ∆px ∆x = h is valid for a particle enclosed in a one-dimensional potential box on condition the momentum change ∆px concerns two neighbouring quantum states. A corresponding change of the particle position coordinate ∆x can be not so small. The relation for ∆px and ∆x obtained for the one-dimensional case can be found to exist also in a three-dimensional system of the hydrogen atom taken as an example.