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

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.

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The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.