Authors: John Shim
This paper notes that the dispersion relation ∇px∇x ≥ ħ/2, when expressed as an equality, ∇px∇x = ħ/2, defines the relationship between the ground-state mean kinetic energy of a confined quantum, and its dimensions of containment. The containment can occur in two ways: the first by an attractive potential, and the second by a repulsive potential. If the quantum is bound by an attractive potential, the ground-state kinetic energy is balanced by the containing potential in a stable state where the kinetic energy remains within the bound system. In the second type, which is only possible by compression, the quantum is contained by collisions with the bounding potential, which may result in a transfer of kinetic energy to the boundary. If the boundary is sufficiently massive, then the energy transfer will have a negligible effect on the dimensions of containment, and therefore the ground-state kinetic energy of the contained quantum will not significantly change. This energy transfer could be large. An electron contained within the approximate diameter of an iron atom, 250 pm, for example, would have a minimum velocity very great compared to the dimension of containment, so that the number of collisions per second with the boundary would be very high, on the order of 10^15. An exchange of only 10^-6 ev per collision would produce 10^9 ev per second of energy transmitted to the boundary.
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