CAN P-ADIC NUMBERS BE USEFUL TO REGULARIZE DIVERGENT EXPECTATION VALUES OF QUANTUM OBSERVABLES

We show how p-adic analysis can be used in some cases to treat diverge nt series in quantum mechanics. We consider examples in which the usua l theory of the Schrodinger equation would give rise to an infinite ex pectation value of the energy operator. By using p-adic analysis, we a re able to get a convergent expansion and obtain a finite rational val ue for the energy. We present also the main ideas to interpret a quant um mechanical state by means of p-adic statistics.