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Rayleigh-Ritz Variational Method in The Complex Plane

arXiv Quantum Physics
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A new study extends the Rayleigh-Ritz variational method to complex-plane quantum oscillators, focusing on Segal-Bargmann space for more accurate energy calculations. The work derives a strict normalizability condition (|α| < ½) for generalized Gaussian trial functions, ensuring convergence in complex Gaussian integrals for quantum harmonic oscillators. For quartic anharmonic oscillators, adaptive Gaussian ansätze in position space yield cubic stationarity equations, improving perturbative energy expansions beyond first-order accuracy. Monomial trial functions (ψₙ(z) = zⁿ) provide rigorous upper bounds for excited states but fail to adapt wavefunction width, limiting ground-state precision to first-order approximations. Displaced Gaussians and monomials better capture asymmetric potentials (e.g., x³ + x⁴), with displacement parameters proving essential for modeling parity-breaking effects and stabilization.
Rayleigh-Ritz Variational Method in The Complex Plane

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Quantum Physics arXiv:2603.02257 (quant-ph) [Submitted on 27 Feb 2026] Title:Rayleigh-Ritz Variational Method in The Complex Plane Authors:M.W. AlMasri View a PDF of the paper titled Rayleigh-Ritz Variational Method in The Complex Plane, by M.W. AlMasri View PDF HTML (experimental) Abstract:We present a systematic study of the Rayleigh--Ritz variational method for quantum oscillators in the Segal--Bargmann space. We rigorously derive the normalizability condition $|\alpha| new | recent | 2026-03 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)

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Source: arXiv Quantum Physics