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Canp-adic numbers be useful to regularize divergent expectation values of quantum observables?

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Abstract

We show howp-adic analysis can be used in some cases to treat divergent series in quantum mechanics. We consider examples in which the usual theory of the Schrödinger equation would give rise to an infinite expectation value of the energy operator. By usingp-adic analysis, we are able to get a convergent expansion and obtain a finite rational value for the energy. We present also the main ideas to interpret a quantum mechanical state by means ofp-adic statistics.

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Cianci, R., Khrennikov, A. Canp-adic numbers be useful to regularize divergent expectation values of quantum observables?. Int J Theor Phys 33, 1217–1228 (1994). https://doi.org/10.1007/BF00670787

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Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Quantum Mechanic
  • Main Idea