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$$p$$-adic numbers and renormalization of eigenfunctions in quantum mechanics. (English) Zbl 0910.46060
Summary: In this paper we show how $$p$$-adic analysis can be used, in some cases, to treat divergent series in quantum mechanics. We shall consider examples in which the usual theory of Schrödinger equation would give rise to an infinite expectation value of the energy operator; on the contrary, by using $$p$$-adic analysis, we are able to get a convergent expansion and obtain a finite rational value for the energy.

##### MSC:
 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis 81Q99 General mathematical topics and methods in quantum theory
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