Nonpointlike Particles in Harmonic Oscillators

Abstract

Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty $\Delta x$ can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation relations induce a finite lower bound to spatial localisation. Here, we perturbatively calculate the corrections to the energy levels of an in this sense nonpointlike particle in isotropic harmonic oscillators. Apart from a special case the degeneracy of the energy levels is removed.

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References in corpus (3)

• Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta
• On Noncommutative Geometric Regularisation
• Unified view of multimode algebras with Fock-like representations

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