量化认识论

Berezin-Toeplitz量子化的例子：有限集和单位区间

Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval

我们提出了一个量子化方案的任意测度空间的基础上过完备的家庭的状态和推广的Klauder和Berezin-Toeplitz方法。该方案可以揭示自己作为一个有效的工具，量化的物理系统，更传统的方法，如几何量化是难以实现的。该程序说明（主要是二维）的基本例子中，测量空间是一个$N$元素集和单位区间。$N$ -元素集和单位间隔的状态空间是2维欧几里德$\R^2$和厄米特$\C^2$平面。

Canonical quantization on the half-line and in an interval based upon a new concept for the momentum in a space with boundaries

For a particle moving on a half-line or in an interval the operator $\hat p = - i \partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. Consequently canonical quantization based on $\hat p$ fails. Based upon a new concept for a self-adjoint momentum operator $\hat p_R$, we show that canonical quantization can indeed be implemented on the half-line and on an interval. Both the Hamiltonian $\hat H$ and the momentum operator $\hat p_R$ are endowed with self-adjoint extension parameters that characterize the corresponding domains $D(\hat H)$ and $D(\hat p_R)$ in the H…

有界集合中的正则化量子运动：希尔伯特空间方面

Regularized quantum motion in a bounded set: Hilbertian aspects

本文研究有界区间内粒子动量算子的本质自伴性问题，提出用正有界函数对称加权动量算子以恢复本质自伴性，并通过Weyl-Heisenberg协变积分量子化从加权经典动量一致地构造该算子。