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AuthorAl-Hashimi, M. H.
AuthorSalman, M.
AuthorShalaby, A. M.
Available date2023-01-22T05:04:41Z
Publication Date2022-01-01
Publication NameInternational Journal of Modern Physics A
Identifierhttp://dx.doi.org/10.1142/S0217751X22501950
ISSN0217751X
URIhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85145470696&origin=inward
URIhttp://hdl.handle.net/10576/38652
AbstractA general method has been developed to solve the Schrödinger equation for an arbitrary derivative of the δ-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A distinction in the treatment has been made between the case when the derivative n is an even number from the one when n is an odd number. A general gap equation for each case has been derived. The case of δ(2)-function potential has been used as an example. The results from the relativistic case show that the δ(2)-function system behaves exactly like the δ-function and the δ′-function potentials, which means it also shares the same features with quantum field theories, like being asymptotically free, in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. As a result, the evidence of universality of contact interactions has been extended further to include the δ(2)-function potential.
SponsorThis paper was made possible by the NPRP grant # NPRP 5-261-1-054 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors.
Languageen
PublisherWorld Scientific Publishing
Subjectcutoff regularization
Relativistic particle interaction
relativistic Schrodinger equation for delta potential n-derivative
TitleThe general solution for the relativistic and nonrelativistic Schrödinger equation for the δ(n) -function potential in 1-dimension using cutoff regularization, and the fate of universality
TypeArticle
Issue Number31n32
ESSN1793-656X
dc.accessType Full Text


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