In reply to Horace Heffner's message of Sat, 5 Jan 2008 15:57:02 -0900: Hi, [snip] >> True, but one is not free to choose the radial direction, because >> that is >> perpendicular to the path of the electron (and hence it's >> momentum). IOW >> whatever dimension one chooses, both momentum and distance must lie >> along the >> same vector, but there is no movement in the radial direction, >> hence it is >> trivially irrelevant. > >If that were true then the de Broglie wavelength would be irrelevant >to any consideration and interference would be impossible because the >de Broglie wavelength existence would only be in the direction of >travel. Interference is due to the *lateral* wave extension, not >longitudinal.
A lateral wave is still possible that lies on the surface of the sphere. De Broglie himself used a phase criterion in the De Broglie wave to calculate the radius of the Hydrogen ground state. > >The HUP limitations apply in any (i.e. every) direction you might >chose, and the de Broli wavelength extends in all directions. If a >particle is constrained to a small volume then it exerts a pressure, >so increasing the confinement results in increasing the pressure, >which requires energy, >and since the situation is constrained by E* >(detla t) = h/(4Pi), > >Correction: the above should say: "the time confined to a small >volume is energy limited unless some supply of energy is available to >create the state of confinement." This is the case. In shrinking to a smaller orbital, electrostatic potential energy becomes available. However, if I'm not mistaken the energy/time form of the HUP pertains to uncertainties in energy and time, not absolute values. Since the position of the electron is indeterminate, so is the time (at any given point), and hence the uncertainty in the time is also infinite, resulting in possible very precise energies. Regards, Robin van Spaandonk The shrub is a plant.
