2001/12/14 by Alexandr Yelnikov, Yelnikov, Alexandr
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0112134
7 pages, 1 figure, RevTeX4
arxiv created 2001/12/14 · openalex publication_date 2001/12/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum mechanics in the presence of δ-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by constructing self-adjoint extensions of the corresponding Hamiltonians. Two particularly interesting examples of this kind are nonrelativistic spin zero particles in δ-function potential and Dirac particles in Aharonov-Bohm magnetic background. In this paper we show that by extending the corresponding Schrödinger and Dirac equations onto the flat noncommutative space a well-defined quantum theory can be obtained. Using a star product and Fock space formalisms we construct the complete sets of eigenfunctions and eigenvalues in both cases which turn out to be finite.