量子力学虚拟实验的MATLAB演示

量子力学是一门较抽象的科学.为了更直观、形象地展示量子力学中的一些物理原理和实验现象,本文利用MAT-LAB软件搭建了一个量子力学的虚拟演示平台,可以生动地演示电子双缝衍射、量子隧穿效应、氢原子电子云和斯塔克效应等现象.通过相关物理参数的输入以及物理现象的演示,可以使学生在量子力学的学习中获得更直观的教学感受.     

工科量子力学学习中的常用数学工具

数学是学习量子力学必不可少的工具,本文主要介绍了工科学生在学习量子力学过程中常要用到的数学工具,为学习该课程的工科学生提供查阅和使用的便利.由于本课程是基础教程,本文主要方便工科学生查阅使用和更好地学习量子力学,对书中涉及的数学知识未进行详尽展开介绍.     

量子力学本科教学演示仪之量子真空场测量

“真空不空”是量子力学区别于经典物理的一个重要内容.这主要是因为真空场的能量小到无法直接测量,通常需要基于平衡零拍探测的量子实验装置进行测量.然而现阶段的大学物理实验教学中缺乏该实验装置,导致学生无法直观理解这一量子力学的基本概念.针对这一问题,本文设计并搭建了基于平衡零拍探测的真空场测量仪,通过光学放大的过程实现真空场起伏的测量.该实验教学仪原理简单,现象直观,操作容易且便于维护,弥补了大学物理中量子力学实验的空白,实现前沿物理在大学物理教学中的拓展.     

用基函数展开法求解一维有限深方势阱模型

用基函数展开法求解了一维有限深方势阱模型,所得结果与在坐标表象中直接求解薛定谔方程所得结果完全一致.重要的是这一求解过程为量子力学中基函数展开方法的教授与学习提供了一个范例,也为量子力学问题的计算机求解的教与学提供了参考.     

利用PhET仿真软件对量子力学中有限深势阱的可视化教学实践

依据PhET仿真软件提供的强大模拟和显示功能,以一维有限深势阱为具体示例,从单势阱束缚态的能级、波函数和概率密度分布,到多势阱的能带和态密度,通过图像直观获得清晰的量子力学图景.以此为基础,设计了基于问题驱动的混合式教学模式的教学流程,结合学习单、虚拟仿真、小组讨论、翻转课堂、教师讲授、提交论文等形式,有效提升学生的学习参与度,实现多元化目标.     

类比、记忆、做题、总结——谈量子力学的一点学习体会

 众所周知,在大学物理学习中,四大力学可谓是重中之重。而论重要性,首推量子力学。经过一个学期的学习,我较好地掌握了量子力学,也总结出了一些学习方法,对很多问题有了较为深刻的理解,下面就自己的学习经过谈一点看法,希望给大家一点启发,与大家共同进步。     

基于光学偏振试验的量子概念分析

量子力学主要描述微小尺度下事物的行为,许多量子现象与人们日常直接经验相悖,因而量子力学的基本概念在教学过程中不容易被学生接受.偏振光实验是一个学生熟知、且实验现象直观的普通物理实验.本文着重从可观测量和测量的角度,通过对光学偏振实验现象的解释来阐述量子概念,使抽象的量子概念落实到对具体实验现象的归纳总结上来,有助于初学者认识和理解量子力学基本原理.     

一维无限深方势阱中粒子动量概率分布引出的问题

本文强调泡利关于一维无限深方势阱中粒子动量的结论与标准量子力学的逻辑推论不一致,而标准量子力学是自洽的。指出,当我们在一个量子态上掺入某种直观的经典力学内容时要很谨慎。至于对量子力学本身,至今尚无一种公认的诠释。     

电子衍射过程的模拟程序

电子或微观粒子的衍射实验不能直观地将衍射过程显示出来．本文所述是模拟电子衍射过程的 ＢＡＳＩＣ语言程序．在 Ａｐｐｌｅ Ⅱ微机上运行时，明确地表现了电子的衍射过程，衍射图样完整清晰，有助于量子力学中对波函数统计意义的理解．     

干涉现象中能量叠加的实验研究

经典的波动理论与量子理论均分别对杨氏双缝干涉实验进行了解释。由于两个解释理论一个简单直观、一个复杂抽象,但两者结果一致,使得学生在学习中容易接受波动理论而排斥量子理论。文中通过实验观测了杨氏双缝干涉光场中能量传递与叠加的实际情况,结果显示实验实际情况与波动理论解释明显不相符合,而与量子理论解释完全相符。通过实验,使学生直观地看到波动理论的局限性,并加深学生对量子力学相关理论的理解。     

The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part III. Idealizations. Hilbert space representation

We illustrate the application of the conceptual analysis (CA) method outlined in Part I by the example of quantum mechanics. In the present part the Hilbert space structure of conventional quantum mechanics is deduced as a consequence of postulates specifying further idealized concepts. A critical discussion of the idealizations of quantum mechanics is proposed. Quantum mechanics is characterized as a “statistically complete” theory and a simple and elegant formal recipe for the construction of the fundamental mathematical apparatus of quantum mechanics is formulated. Our analysis may also lead to a criticism of quantum mechanics as a “strongly idealized” theory. A critical analysis of the fundamental structure of quantum mechanics seems an indispensable and natural starting point for the construction of new theories. A major technical problem in a more general application of the CA method is the lack of mathematical representation theorems for more general algebraic structures.     

Quantum Physics and Classical Physics—In the Light of Quantum Logic

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can be established which is given by an orthomodular lattice. By means of the Solèr condition and Piron's result one obtains the classical Hilbert spaces. However, this approach is not fully convincing. There is no plausible justification of Solèr's law and the quantum ontology is partly too weak and partly too strong. We propose to replace this ontology by an ontology of unsharp properties and conclude that quantum mechanics is more intuitive than classical mechanics and that classical mechanics is not the macroscopic limit of quantum mechanics.     

Understanding quantum entanglement: Qubits,rebits and the quaternionic approach

It has been recently pointed out by Caves, Fuchs, and Rungta [1] that real quantum mechanics (that is, quantum mechanics defined over real vector spaces [2–5]) provides an interesting foil theory whose study may shed some light on just which particular aspects of quantum entanglement are unique to standard quantum theory and which are more generic over other physical theories endowed with this phenomenon. Following this work, some entanglement properties of two-rebit systems are discussed and a comparison with the basic properties of two-qubit systems, i.e., the systems described by standard complex quantum mechanics, is made. The use of quaternionic quantum mechanics as applied to the phenomenon of entanglement is also discussed.     

氢原子的固有电偶极矩

用经典力学和双波量子力学计算了氢原子的固有电偶极矩。双波量子理论算得的结果在经典极限下与经典力学的结果一致。普通量子力学对氢原子Stark效应中表现出来的电偶极矩难以做出很好的解释，因为一个波函数描述的是系综而不是单个粒子。经典力学和双波量子力学可描述单个粒子的行为，对永久电偶极矩的计算和解释显得自然而合理。     

Statistics of Local Value in Quantum Mechanics

Given a quantum mechanical observable and a state, one can construct a classical observable, that is, a real function on the configuration space, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. This optimal estimate turns out to be the quantum mechanical local value, which arises from several contexts such as de Broglie–Bohm's casual approach to quantum mechanics, instantaneous frequency in time–frequency analysis, Nelson's quantum fluctuations formalism, and phase-space approach to quantum mechanics. Accordingly, any observable can be decomposed into a local value part and a quantum fluctuation part, which are independent, both geometrically and statistically. Furthermore, the current density in quantum mechanics, the osmotic velocity in stochastic mechanics, and the Fisher information in classical statistical inference, arise naturally in connection with local value. In particular, Heisenberg uncertainty principle can be quantified more precisely by virtue of local value.     

On the precision of a length measurement

We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the discreteness of spacetime on lengths shorter than the Planck length. We then consider the fundamental limit coming from quantum mechanics, general relativity and causality on the precision of length measurement. PACS 04.20.-q; 03.65.-w     

Mathematical foundations of quantum field theory: Fermions,gauge fields,and supersymmetry part I: Lattice field theories

In this paper we explore the mathematical foundations of quantum field theory. From the mathematical point of view, quantum field theory involves several revolutions in structure just as severe as, if not more than, the revolutionary change involved in the move from classical to quantum mechanics. Ordinary quantum mechanics is based upon real-valued observables which are not all compatible. We will see that the proper mathematical understanding of Fermi fields involves a new concept of probability theory, the graded probability space. This new concept also yields new points of view concerning ergodic theorems in statistical mechanics.     

Quaternionic quantum mechanics is consistent with complex quantum mechanics

Quaternionic quantum mechanics is investigated in the light of the great success of complex quantum mechanics. It is shown that to reproduce the results of complex quantum mechanics, quaternionic quantum mechanics must contain complex quantum mechanics.     

Quantum Logic Gates and Nuclear Magnetic Resonance Pulse Sequences

There has recently been considerable interest in the use of nuclear magnetic resonance (NMR) as a technology for the implementation of small quantum computers. These computers operate by the laws of quantum mechanics, rather than classical mechanics and can be used to implement new quantum algorithms. Here we describe how NMR in principle can be used to implement all the elements required to build quantum computers, and draw comparisons between the pulse sequences involved and those of more conventional NMR experiments.