论文标题
通过量子组的非架构量子力学
Non-Archimedean Quantum Mechanics via Quantum Groups
论文作者
论文摘要
我们提出了一种新的非架构的实现Q振荡者代数的FOCK表示，其中创建和歼灭操作员作用于复杂值函数，该功能是在非架构的局部局部特征领域中定义的，例如，P-Adic数字的字段。这种新的认识意味着，使用Q振荡器代数构建的大量量子模型是非一切型模型，尤其是P-ADIC量子模型。在此框架中，我们选择了海森堡不确定性关系的Q-信息，并构建相应的Q构造的Schrödinger方程。通过这种方式，我们构建了一种P-Adic量子力学，该量子力学是一种P-pemformed的量子力学。我们还解决了自由粒子的时间无关的schrödinger方程，以及在非架构盒中的粒子。在最后一个情况下，我们显示了一个离散序列的存在。我们确定Schrödinger操作员的特征值，以获得一般的径向电势。通过以合适形式选择电势，我们恢复了Q-氢原子的能级。
We present a new non-Archimedean realization of the Fock representation of the q-oscillator algebras where the creation and annihilation operators act on complex-valued functions, which are defined on a non-Archimedean local field of arbitrary characteristic, for instance, the field of p-adic numbers. This new realization implies that a large number of quantum models constructed using q-oscillator algebras are non-Archimedean models, in particular, p-adic quantum models. In this framework, we select a q-deformation of the Heisenberg uncertainty relation, and construct the corresponding q-deformed Schrödinger equations. In this way we construct a p-adic quantum mechanics which is a p-deformed quantum mechanics. We also solve the time-independent Schrödinger equations for the free particle, and a particle in a non-Archimedean box. In the last case we show the existence of a discrete sequence of energy levels. We determine the eigenvalues of Schrödinger operator for a general radial potential. By choosing the potential in a suitable form we recover the energy levels of the q-hydrogen atom.
