arXiv 2302.021722023-02-04quant-ph

具有位置依赖质量的非对称振子的精确解和相干态

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

Bruno G. da Costa, Ignacio S. Gomez, Biswanath Rath

备注：: 24 pages, 11 figures
发表信息：: J. Math. Phys. 64, 012102 (2023)
DOI：: 10.1063/5.0094564

摘要：

我们重新讨论了具有位置依赖质量的变形振子的问题[da Costa et al.，J. Math. Phys. { \bf 62}，092101（2021）]中，通过在动能和势能中引入质量函数的影响。通过点正则变换，从通常的相空间$(x, p)$映射到变形的相空间$(x_γ, Π_γ)$，从而将所得的哈密顿量映射到Morse振子中.与Morse势类似，变形振子在相空间中呈现出与经典形式主义中的非谐振荡运动相对应的束缚轨道，因此，在量子形式主义中呈现出具有离散谱的束缚态。另一方面，相空间中的开放轨道与散射态和连续的能谱相关联。利用因式分解方法，我们研究了相干态的时间演化及其不确定性等性质。由于非对称的位置依赖质量，一个快速的局域化，经典和量子，报告的相干态。还观察到的不确定性关系的时间演化的振荡，其幅度随着变形的增加而增加。

英文摘要：

We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space $(x, p)$ to a deformed one $(x_γ, Π_γ)$. Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.

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