## 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.

### MSC:

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

### Keywords:

non-pointlike particles; harmonic oscillators
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