Quasi-harmonic spectra from branched Hamiltonians
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914229615853568 |
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| author | Ghosh, Aritra Bagchi, Bijan Ghose-Choudhury, A. Guha, Partha Znojil, Miloslav |
| author_facet | Ghosh, Aritra Bagchi, Bijan Ghose-Choudhury, A. Guha, Partha Znojil, Miloslav |
| contents | We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + ω^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Liénard-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-harmonic spectra from branched Hamiltonians Ghosh, Aritra Bagchi, Bijan Ghose-Choudhury, A. Guha, Partha Znojil, Miloslav Quantum Physics Mathematical Physics Exactly Solvable and Integrable Systems We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + ω^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Liénard-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. |
| title | Quasi-harmonic spectra from branched Hamiltonians |
| topic | Quantum Physics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2512.22510 |