p-adic numbers and renormalization of eigenfunctions in quantum mechanics

Abstract 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 Schrodinger equation would give rise to an infinite for the 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.