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Can \(p\)-adic numbers be useful to regularize divergent expectation values of quantum observables? (English) Zbl 0842.60096

Summary: We show how \(p\)-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 using \(p\)-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 of \(p\)-adic statistics.

MSC:

60K40 Other physical applications of random processes
60A99 Foundations of probability theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
11S85 Other nonanalytic theory
11Z05 Miscellaneous applications of number theory
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