Collapse and transition of a superposition of states under a delta-function pulse in a two-level system
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Quantum Physics arXiv:2603.02407 (quant-ph) [Submitted on 2 Mar 2026] Title:Collapse and transition of a superposition of states under a delta-function pulse in a two-level system Authors:Ariel Edery View a PDF of the paper titled Collapse and transition of a superposition of states under a delta-function pulse in a two-level system, by Ariel Edery View PDF HTML (experimental) Abstract:Under a time-dependent perturbation it is common to calculate the transition probability in going from from one eigenstate to another eigenstate of a quantum system. In this work we study the transition in going from a \textit{linear superposition of eigenstates} to an eigenstate under a delta-function pulse (which acts at $t=0$). We consider a two-level system with energy levels $E_1$ and $E_2$ and solve the coupled set of first order equations to obtain exact analytical expressions for the coefficients $c_1(t>0)$ and $c_2(t>0)$ of the final state. The expressions for the final coefficients are general in the sense that they are functions of the interaction strength $\beta$ and the coefficients $\alpha_1$ and $\alpha_2$ of the initial superposition state which are free parameters constrained only by $|\alpha_1|^2+ |\alpha_2|^2=1$. This opens up new possibilities and in particular, allows for a ``collapse" scenario. We obtain a general analytical expression for the transition probability $P_{\alpha_1,\alpha_2 \to 2}$ in going from an initial superposition state to the second eigenstate. Armed with this general expression we study some interesting special cases. With a delta-function pulse, the transitions are abrupt/instantaneous and we show that they do not depend on the energy gap $E_2-E_1$ and hence on the relative phase between the two eigenstates. For specific multiple values of the interaction strength $\beta$, we show that the system ends up in a definite eigenstate i.e. probability of unity. Such a transition can be viewed as a ``collapse" since a superposition of states transitions abruptly to a definite eigenstate. The collapse of the wavefunction is familiar in the context of a measurement. Here it occurs via a delta-function pulse in Schrödinger's equation. We discuss how this differs from a collapse due to a measurement. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2603.02407 [quant-ph] (or arXiv:2603.02407v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.02407 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ariel Edery [view email] [v1] Mon, 2 Mar 2026 21:33:25 UTC (47 KB) Full-text links: Access Paper: View a PDF of the paper titled Collapse and transition of a superposition of states under a delta-function pulse in a two-level system, by Ariel EderyView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: hep-th 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?)