Exact classical emergence from high-energy quantum superpositions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916049051451392 |
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| author | Cañas, Juan A. Bonilla, Daniel A. Bernal, J. Martín-Ruiz, A. |
| author_facet | Cañas, Juan A. Bonilla, Daniel A. Bernal, J. Martín-Ruiz, A. |
| contents | We examine the correspondence principle for an equiprobable superposition of high-energy eigenstates of the infinite square well using a fully analytical Fourier-based approach. We derive a closed-form asymptotic expression for the interference terms $ρ_α^{\text{a}}(x)$ by expanding them into a geometric series of quantum Fourier coefficients. We show these terms act as functional envelopes that do not vanish individually but become asymptotically equivalent in the large-$n$ limit. Furthermore, we prove the total probability density for a superposition of $2Δ+1$ states converges exactly to the uniform classical distribution as $Δ\to \infty$. Dynamically, the expectation value of position reproduces the classical triangular trajectory asymptotically. Residual quantum deviations remain confined to boundary layers whose relative width vanishes under macroscopic resolution. These results establish a rigorous asymptotic realization of the classical limit for isolated bound systems in both static and dynamical contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16518 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact classical emergence from high-energy quantum superpositions Cañas, Juan A. Bonilla, Daniel A. Bernal, J. Martín-Ruiz, A. Quantum Physics Mathematical Physics We examine the correspondence principle for an equiprobable superposition of high-energy eigenstates of the infinite square well using a fully analytical Fourier-based approach. We derive a closed-form asymptotic expression for the interference terms $ρ_α^{\text{a}}(x)$ by expanding them into a geometric series of quantum Fourier coefficients. We show these terms act as functional envelopes that do not vanish individually but become asymptotically equivalent in the large-$n$ limit. Furthermore, we prove the total probability density for a superposition of $2Δ+1$ states converges exactly to the uniform classical distribution as $Δ\to \infty$. Dynamically, the expectation value of position reproduces the classical triangular trajectory asymptotically. Residual quantum deviations remain confined to boundary layers whose relative width vanishes under macroscopic resolution. These results establish a rigorous asymptotic realization of the classical limit for isolated bound systems in both static and dynamical contexts. |
| title | Exact classical emergence from high-energy quantum superpositions |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2605.16518 |