Quantum Physics


Compton-Wavelength Minimum Position Uncertainty Due to Diversion of Momentum Uncertainty to Increased Particle Number

Authors: Steven Kenneth Kauffmann

In single-particle quantum mechanics there is no impediment to a particle's wave function having a significant amplitude for arbitrarily short wavelengths, i.e., for arbitrarily large momenta, so the iconic single-particle uncertainty relation permits a particle's position to be arbitrarily accurately ascertained. Once a single-particle theory is second quantized, however, the physics of imparting a particle's wave function with ever larger momenta eventually encounters stiff competition from the formation of multiparticle states wherein none of the individual particles is characterized by high momentum. In fact, the single-particle uncertainty principle itself is modified by the presence of the expectation value of the particle number operator on its right side. Since the threshold for the high-momentum-diverting formation of additional particles is set by the particle's rest mass, it stands to reason that particles have an irreducible position uncertainty of the order of their Compton wavelength, for which we develop a specific model.

Comments: 6 Pages.

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Submission history

[v1] 2019-06-27 15:25:48

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