Summary
The mathematical aspects of singular potentials in nonrelativistic quantum mechanics are studied in terms of the self-adjoint transformations related to singular differential operators in the space L2(0, ∞). The physical content is expressed by the spectral decompositions and for attractive potentials found to be determined only up to a parameter denning a particular extension. In general it is not possible to determine a specific extension by a cut-off procedure.
Riassunto
Si studiano gli aspetti matematici dei potenziali singolari nella meccanica quantistica non relativistica in funzione delle trasformazioni autoaggiunte riferite a operator! differenziali singolaii nello spazio L2(0, ∞). Il contenuto fisico è espresso dalla decomposizione spettrale e per potenziali attrattivi si trova che è determinate solo sino ad un parametro che definisce una particolare estensione. In generale, con un procedimento di taglio non è possibile determinare un’estensione specifica.
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Meetz, K. Singular potentials in nonrelativistic quantum mechanics. Nuovo Cim 34, 690–708 (1964). https://doi.org/10.1007/BF02750010
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DOI: https://doi.org/10.1007/BF02750010