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arXiv · 2512.22510

Quasi-harmonic spectra from branched Hamiltonians

Aritra Ghosh·Bijan Bagchi·A. Ghose-Choudhury·Partha Guha·Miloslav Znojil
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Abstract

We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + \omega^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Li\'enard-Kukles equation. While its classical isochronicity and canonical quantization, leading to polynomial solutions with an exactly-equispaced spectrum have been discussed earlier, including in the recent paper [Int. J. Theor. Phys. 64, 212 (2025)], the present study focuses on the quantization of its branched Hamiltonians. For small $k$, we show numerically that the resulting energy spectrum is no longer perfectly harmonic but only approximately equispaced, exhibiting quasi-harmonic behavior characterized by deviations from uniform spacing. Our numerical results are precisely validated by analytical calculations based on perturbation theory.

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Aritra Ghosh, Bijan Bagchi, A. Ghose-Choudhury, Partha Guha, Miloslav Znojil. 2025-12-27. Quasi-harmonic spectra from branched Hamiltonians. https://doi.org/10.1016/j.physleta.2025.131289

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