Exact lower bound of the uncertainty principle product for the harmonic oscillator with position-momentum coupling
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911775627149312 |
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| author | Hamdouni, Yamen |
| author_facet | Hamdouni, Yamen |
| contents | We show that the uncertainty principle product for the position and momentum operators for a system described by the Hamiltonian $ \hat H= \frac{\hat{p}^2}{2m} +\frac{1}{2} m ω^2 \hat{x}^2+\fracμ{2}(\hat x \hat p+ \hat p \hat x)$ where $μ<ω$ reads $Δx Δp\ge\frac{\hbar ω}{2\sqrt{ω^2-μ^2}}$. All the values bellow this lower bound are thus quantum-mechanically forbidden. We construct the annihilation and creation operators for this system and we calculate the expectation values of the operators $\hat p$ and $\hat x$ with respect to the corresponding coherent states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact lower bound of the uncertainty principle product for the harmonic oscillator with position-momentum coupling Hamdouni, Yamen Quantum Physics Mathematical Physics We show that the uncertainty principle product for the position and momentum operators for a system described by the Hamiltonian $ \hat H= \frac{\hat{p}^2}{2m} +\frac{1}{2} m ω^2 \hat{x}^2+\fracμ{2}(\hat x \hat p+ \hat p \hat x)$ where $μ<ω$ reads $Δx Δp\ge\frac{\hbar ω}{2\sqrt{ω^2-μ^2}}$. All the values bellow this lower bound are thus quantum-mechanically forbidden. We construct the annihilation and creation operators for this system and we calculate the expectation values of the operators $\hat p$ and $\hat x$ with respect to the corresponding coherent states. |
| title | Exact lower bound of the uncertainty principle product for the harmonic oscillator with position-momentum coupling |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2402.07842 |