Heisenberg Uncertainty Principle for Momentum and Position Coordinates Referred to the Joule-Lenz Relation for Energy and Time

  • Stanisław Olszewski


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.