论文标题
$ \ MATHCAL {P} \ MATHCAL {T} $ - 用于位置依赖有效质量的对称量子系统违反Heisenberg不确定性原理
$\mathcal{P}\mathcal{T}$-symmetric Quantum systems for position-dependent effective mass violate the Heisenberg uncertainty principle
论文作者
论文摘要
我们已经研究了一个$ \ Mathcal {p} \ Mathcal {t} $ - 一类依赖位置的有效质量的对称量子系统。超对称量子力学的形式主义用于构建伴侣电位。由于所考虑的系统不是自我偶像，因此交织的操作员不会分解哈密顿量。我们借助广泛的an灭和创建操作员将哈密顿量分解，该操作员作用于变形的坐标和动量空间。该系统的相干状态结构是由广义歼灭操作员的本征构建的。 \\事实证明，自偶会变形的位置和动量操作员违反了$ \ Mathcal {p} \ Mathcal {t} $对称系统的Heisenberg不确定性原理。这种违规仅取决于$ \ MATHCAL {P} \ MATHCAL {T} $ - 对称术语，而不取决于内部产品的选择。对于明确的构造，我们已经证明，为简单起见，恒定的质量$ \ MATHCAL {p} \ MATHCAL {t} $ - 对称系统谐波振荡器，该振荡器违反了可接受的参数值的不确定性原理。结果表明，$ \ MATHCAL {P} \ MATHCAL {T} $ - 对称系统是通常的量子力学的琐碎扩展，或者仅适用于开放量子系统。
We have studied a $\mathcal{P}\mathcal{T}$-symmetric quantum system for a class of position-dependent effective mass. Formalisms of supersymmetric quantum mechanics are utilized to construct the partner potentials. Since the system under consideration is not self-adjoint, the intertwining operators do not factorize the Hamiltonian. We have factorized the Hamiltonian with the aid of generalized annihilation and creation operators, which acts on a deformed coordinate and momentum space. The coherent state structure for the system is constructed from the eigenstates of the generalized annihilation operator. \\ It turns out that the self-adjoint deformed position and momentum operators violate the Heisenberg uncertainty principle for the $\mathcal{P}\mathcal{T}$-symmetric system. This violation depends solely on the $\mathcal{P}\mathcal{T}$-symmetric term, not on the choice of the inner product. For explicit construction, we have demonstrated, for simplicity, a constant mass $\mathcal{P}\mathcal{T}$-symmetric system Harmonic oscillator, which shows the violation of the uncertainty principle for a choice of acceptable parameter values. The result indicates that either $\mathcal{P}\mathcal{T}$-symmetric systems are a trivial extension of usual quantum mechanics or only suitable for open quantum systems.
