论文标题
具有可变质量的密闭系统的量子和半古典方面
Quantum and semi-classical aspects of confined systems with variable mass
论文作者
论文摘要
我们探讨了具有依赖位置质量（PDM）项的经典模型的量化，这些术语约束至规范位置的有限间隔。这是通过在相位空间上正确选择正规化函数$π（q，p）$的Weyl-Heisenberg协变量量化实现的，从而平滑了经典模型中存在的不连续性。因此，我们获得了明确定义的操作员，而无需建立自我伴侣扩展。同时，量化机制自然导致了半古典系统，即具有明确定义的哈密顿结构的经典模型，在这种模型中，普朗克常数的影响不可忽略不计。有趣的是，对于非分离函数$π（q，p）$，纯量子最小耦合项以量子和半古典模型的矢量电位形式出现。
We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly choosing a regularizing function $Π(q,p)$ on the phase space that smooths the discontinuities present in the classical model. We thus obtain well-defined operators without requiring the construction of self-adjoint extensions. Simultaneously, the quantization mechanism leads naturally to a semi-classical system, that is, a classical-like model with a well-defined Hamiltonian structure in which the effects of the Planck's constant are not negligible. Interestingly, for a non-separable function $Π(q,p)$, a purely quantum minimal-coupling term arises in the form of a vector potential for both the quantum and semi-classical models.
