当前位置: X-MOL 学术Commun. Nonlinear Sci. Numer. Simul. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Quantization method and Schrödinger equation of fractional time and their weak effects on Hamiltonian: Phase transitions of energy and wave functions
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-09-09 , DOI: 10.1016/j.cnsns.2020.105531
Xiao Zhang , Bo Yang , Chaozhen Wei , Maokang Luo

Fractional time quantum mechanics (FTQM) is a method of describing the time evolution of quantum dynamics based on fractional derivatives. For any potential, we obtain the modeling method to describe quantum systems with fractional time consistent with fundamental quantum physics laws, which makes fractional time effects naturally enter quantum mechanics. The method is only using the start states, not based on usually directly replacing the integer derivatives by fractional ones or parallel introductions of standard models. In the process, we solve three open problems perplexing the studies on FTQM: What is the essential quantization method? How does one represent the fractional time Hamiltonian while retaining physical significance? How does one avoid the violations of current models of FTQM for many fundamental quantum physics laws? Then, a FTQM framework is built by amalgamating two quantization methods under a unified foundation of fractional time. The framework contains the quantization method, the Hamiltonian, the Hamilton operator, the Schrödinger equation, the energy correspondence relation, the Bohr correspondence principle and the time-energy uncertainty relation. And the effects of fractional time are revealed: containing historical information of particle’s motions; representing weak actions of Hamilton operator. An example is provided, and analytic expressions of the energy and wave functions are obtained. These account for the distinct nonlinear phenomena: the phase transition of energy and wave functions, which can not be revealed in the previous methods. The phase transitions cause some classical physical effects and phenomena: (1) energy gaps filled by energy levels; (2) increase in particle orbits; (3) a famous bound states in continuum (BICs) firstly found in FTQM; (4) a new explanation of the discrete energy levels from the perspective of energy level filling.



中文翻译:

分数时间的量化方法和Schrödinger方程及其对哈密顿量的弱影响:能量和波函数的相变

分数时间量子力学(FTQM)是一种基于分数导数描述量子动力学的时间演化的方法。对于任何潜能,我们都获得了用分数时间描述基本量子物理学定律的量子系统的建模方法,这使得分数时间效应自然地进入了量子力学。该方法仅使用开始状态,而不是通常基于分数模型或标准模型的并行引入直接替换整数导数。在此过程中,我们解决了困扰FTQM研究的三个开放问题:什么是基本量化方法?如何在保留物理意义的同时表示分数时间哈密顿量?如何避免许多基本量子物理学定律违反当前的FTQM模型?然后,FTQM框架是通过在分数时间的统一基础上将两种量化方法合并而成的。该框架包含量化方法,哈密顿量,哈密顿算子,薛定ding方程,能量对应关系,玻尔对应原理和时间-能量不确定性关系。并揭示了分数时间的影响:包含粒子运动的历史信息;表示汉密尔顿算子的弱动作。提供了一个示例,并获得了能量和波动函数的解析表达式。这些解释了独特的非线性现象:能量和波函数的相变,这在以前的方法中无法揭示。相变会引起一些经典的物理效应和现象:(1)由能级填充的能隙;(2)增加粒子轨道;(3)FTQM中首次发现了著名的连续体界(BIC);(4)从能级填充的角度对离散能级进行了新的解释。

更新日期:2020-09-09
down
wechat
bug