The Inverted Dirac-Moshinsky Oscillator in $(1+1)$ Dimensions
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Quantum Physics arXiv:2606.02637 (quant-ph) [Submitted on 31 May 2026] Title:The Inverted Dirac-Moshinsky Oscillator in $(1+1)$ Dimensions Authors:Kevin Hernández, Marcos Orellana-Iraheta, William Larín-Escobar View a PDF of the paper titled The Inverted Dirac-Moshinsky Oscillator in $(1+1)$ Dimensions, by Kevin Hern\'andez and Marcos Orellana-Iraheta and William Lar\'in-Escobar View PDF HTML (experimental) Abstract:We derive and analyze the exact solutions of the inverted Dirac-Moshinsky oscillator (IDMO) in $(1+1)$ dimensions, obtained from the standard model via the substitution $p \to p + im\omega\beta x$. The upper spinor component satisfies a Weber equation with complex spectral parameter $\lambda = (E^2-m^2)/(2m\omega)+i/2$, whose solutions are parabolic cylinder functions $D_\nu(\xi)$ with complex order $\nu = \lambda - 1/2$. The physical spectrum is purely continuous ($|E|>m$), with no discrete bound states. Three normalization schemes are developed, and the discrete Gamow resonances at $E_n^\pm = \pm\sqrt{m^2+(2n+1)m\omega-im\omega}$ are identified as poles of the resolvent. The negative-energy sector describes antiparticle anti-resonances whose positive imaginary part signals vacuum instability and spontaneous pair production, analogous to the Schwinger effect. The algebraic structure is governed by the principal series of $SU(1,1)$, and the Hamiltonian is $\mathcal{PT}$-symmetric with unbroken symmetry for $|E|>m$. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2606.02637 [quant-ph] (or arXiv:2606.02637v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.02637 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kevin Giovanni Hernández Beltrán [view email] [v1] Sun, 31 May 2026 03:04:27 UTC (104 KB) Full-text links: Access Paper: View a PDF of the paper titled The Inverted Dirac-Moshinsky Oscillator in $(1+1)$ Dimensions, by Kevin Hern\'andez and Marcos Orellana-Iraheta and William Lar\'in-EscobarView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)