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arXiv · 2605.16518

Exact classical emergence from high-energy quantum superpositions

Juan A. Cañas·Daniel A. Bonilla·J. Bernal·A. Martín-Ruiz
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Abstract

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 $\rho_{\alpha}^{\text{a}}(x)$ 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 $2\Delta+1$ states converges exactly to the uniform classical distribution as $\Delta \to \infty$. 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.

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Juan A. Cañas, Daniel A. Bonilla, J. Bernal, A. Martín-Ruiz. 2026-05-15. Exact classical emergence from high-energy quantum superpositions. https://doi.org/10.1016/j.physleta.2026.131810

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