研究性教学课堂经验交流——关于13.6eV的讲授

本文围绕氢原子基态能级，分别从玻尔理论、定态薛定谔方程及不确定关系三个方面对其做了讨论．这是使用“大学物理学”教材中的部分课堂讲授内容，目的是想说明在具体教学中怎样带领并启发学生以研究的眼光学习，掌握知识，使学生对学科发生兴趣．     

氢原子径向波函数的“初等”解法

用构造氢原子径向波函数的方法,通过解薛定谔方程给出氢原子径向波函数幂多项式的系数．     

氢原子和谐振子的能级、波函数的联系

求氢原子和谐振子的能级、波函数是解两个不同的定态薛定谔方程的问题。实际上，我们从三维谐振子的径向方程出发，应用适当的变换，就能由三维谐振子的能级和波函数导出氢原子与类氢离子的能级和波函数．     

复合斯特恩-盖拉赫实验中的量子力学基本原理

从一个复合斯特恩-盖拉赫实验装置的结果分析,逐步引入量子力学的基本知识,包括二维希尔伯特空间中波函数、自旋算符具体形式、态叠加原理,测量理论、不确定关系和波函数随时间演化的薛定谔方程等。     

一维、二维、三维氢原子能级和电子分布概率

通过一维、二维氢原子定态薛定谔方程的严格解得出的能级公式和波函数，分析了一维、二维氢原子能级特点、简并度和电子分布概率，并将它们与三维氢原子进行比较，发现一维、二维、三维氢原子能级和电子分布概率有许多不同之处。     

创立量子力学的创造活动

１９１１年，卢瑟福提出原子的核式结构学说．玻尔受此启发，于１９１２年提出氢原子中核外电子绕核的轨道运动模型，但是人们不知道如何去寻找复杂原子中的量子化条件．怎样才能发展玻尔轨道的思想，使之能适合除氢原子以外的更复杂的原子呢？为此，薛定谔、海森堡和狄拉...     

基于图形处理器加速数值求解三维含时薛定谔方程

量子力学领域中对强激光场与原子分子相互作用的理论研究非常依赖于数值求解含时薛定谔方程.本文在强场电离的背景下并行求解氢原子的三维含时薛定谔方程.基于球极坐标系,采用分裂算符-傅里叶变换方法将含时薛定谔方程进行了离散化.由此可得到长度规范下的光电子连续态波函数.图形处理器(GPU)可以依托多线程结构充分发挥细粒度并行的优势,实现整体算法的并行加速.计算表明,相对于中央处理器(CPU), GPU并行计算有着最高约60倍的加速比.由此可见,基于GPU加速数值求解三维含时薛定谔方程能够显著缩短计算耗费的时间.这一工作对利用GPU快速求解三维含时薛定谔方程有着重要的指导意义.     

一种简捷求解定态薛定谔方程的方法:科尔-霍普夫变换法

介绍一种求解各个能级及定态波函数的简捷方法,即借助于科尔-霍普夫(Cole-Hopf)变换法,将给定势函数的定态薛定谔方程变换成黎卡提(Riccati)方程,以求出各个能级及定态波函数.并以谐振子、球谐振子、氢原子、P schl-Teller势、Morse势、Hulth啨n势、双原子分子的三参量势函数、同调谐振子为实例,给出求解方法及结果.     

应用量子理论方法研究中子双缝衍射

通过严格求解薛定谔方程得到狭缝中的中子波函数,由基尔霍夫定律得到中子衍射波函数.最后得到中子双缝相对衍射强度与衍射图样位置之间的解析关系.计算所得结果与实验数据符合较好. 关键词： 中子衍射 薛定谔方程 基尔霍夫定律     

玻尔理论与量子力学矛盾析

众所周知，玻尔理论与量子力学在处理氢原子结构时存在着某些不同的结论．本文从波粒二象性和不确定关系出发，解释了存在不同结论的原因，从而进一步阐明了两者之间的联系和本质的区别．     

On the theory of hyperfine structure of atomic levels

A relativistic wave equation is proposed whose solution leads to the appearance of hyperfine structure of levels of an electron in a Coulomb field. This structure is due to the difference between the magnetic moment of an electron and the Bohr magneton. The results of calculations are compared with data obtained by precise laser spectroscopy of the hydrogen atom. It is shown that the calculated spectra are in agreement with the experimental data.     

Copenhagen quantum mechanics

In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists’ laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr’s quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.     

Theory of Atom Optics: Feynman’s Path Integral Approach

The present theory of atom optics is established mainly on the Schrödinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman’s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth’s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach-Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov-Casher effect, the Kapitza-Dirac diffraction effect, and the Aharonov-Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.     

Quasiclassical approach to the interpretation of the Barkas effect

A correction to the Bohr formula making it possible to explain the difference between the stopping powers of positively and negatively charged particles (the Barkas effect) is obtained in the quasiclassical approximation taking into account the difference between electron motion in a hydrogen atom as a function of the charge sign of the moving particle. The influence on the atomic electron of the moving particle leads to a change in the contribution of the adiabatic interaction, in the case of which the energy is not transferred in the majority of collisions, which is the reason for a decrease in the energy losses of slow particles compared with Bohr theory. The results of calculations show that the energy losses per path length unit can be represented in the form of the product of two functions, namely, the energy loss function (in accordance with Bohr theory) and the dynamic function taking into account corrections related to correction of the electron position in the target atom during the collision. Calculations carried out within the framework of classical dynamics make it possible to qualitatively estimate differences between the interaction of protons and antiprotons with target material atoms.     

利用色散法探索玻尔氢原子理论测量普朗克常数

普朗克常数是物理学中一个重要的常数,利用测角仪器分光计,探索用玻尔氢原子理论来测普朗克常数。根据最小偏向角测量三棱镜折射率的原理,利用分光计测量三棱镜的折射率来研究光的色散规律,测量棱镜材料对不同波长入射光的折射率,得到棱镜材料的色散曲线和拟合方程。根据玻尔的氢原子理论,用分光计测出氢原子光谱四条谱线（α,β,γ,δ）的偏向角对应的折射率,由科西经验公式计算出相应的波长。     

Realization of localized Bohr-like wave packets

We demonstrate a protocol to create localized wave packets in very-high-n Rydberg states which travel in nearly circular orbits around the nucleus. Although these wave packets slowly dephase and eventually lose their localization, their motion can be monitored over several orbital periods. These wave packets represent the closest analog yet achieved to the original Bohr model of the hydrogen atom, i.e., an electron in a circular classical orbit around the nucleus. The possible extension of the approach to create "planetary atoms" in highly correlated stable multiply excited states is discussed.     

二维氢原子中的基态奇异特性数值精确对角化法

利用数值有限差分法处理二维氢原子的基态波函数时,计算结果发现其存在着数值奇异特性.本文通过构造一套具有正交完备性的离散贝塞尔基函数,并结合基于Lanczos技术的数值精确对角化方法研究二维氢原子中的基态波函数的数值奇异特性,得到的波函数数值解及其相应的本征能量均与解析结果相一致.这套新的完备的离散贝塞尔基函数,可以在研究一些波函数具有数值奇异特性的体系中发挥至关重要的作用.     

用旋量零标架方法计算氢原子能级

本文用旋量零标架方法计算相对论性氢原子能级,所得结果与Γ矩阵方法算得的结果一样,但不明显地使用任何对易关系。 关键词：     

Study of Bohr–Mottelson with minimal length effect for Q-deformed modified Eckart potential and Bohr–Mottelson with Q-deformed quantum for three-dimensional harmonic oscillator potential

Bohr–Mottelson Hamiltonian on the γ-rigid regime for Q-deformed modified Eckart and three-dimensional harmonic oscillator potentials in the β-collective shape variable was investigated in the presence of minimal length formalism and Q-deformed of the radial momentum part. By introducing new wave function and using the Q-deformed potential concept in Bohr–Mottelson Hamiltonian in the minimal length formalism, the un-normalized wave function and energy spectra equation were obtained by using the hypergeometric method. Meanwhile, the Bohr–Mottelson Hamiltonian in the presence of the quadratic spatial deformation to the momentum in collective shape variable was investigated using transformation of a new variable such as the Schrodinger-like equation with shape invariant potential. The energy equation and un-normalized wave function were obtained using the hypergeometric method. The results showed that the Bohr–Mottelson equations with different energy potentials and different deformation forms in the radial momentum reduced to the similar Schrodinger-like equation with the modified Poschl–Teller potential.