Non-pointlike particles in harmonic oscillators. (English) Zbl 0930.58026

Summary: Quantum mechanics usually describes particles as being pointlike in the sense that, in principle, the uncertainty \(\Delta x\) can be made arbitrarily small. Studies on string theory and quantum gravity motivate correction terms to the uncertainty relations which induce a finite lower bound \(\Delta x_0\) to spatial localization. This structure is implemented into quantum mechanics through small correction terms to the canonical commutation relations. We calculate the perturbations to the energy levels of a particle which is non-pointlike in this sense in isotropic harmonic oscillators, where we find a characteristic splitting of the usually degenerate energy levels. Possible applications are outlined.


58Z05 Applications of global analysis to the sciences
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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