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Table of Content
20 September 2022 Volume 41 Issue 9
Effects of cohesion energy on properties of lattice dynamics
CHEN Feng-liang, FAN Wei-jia, ZHOU Shi-ming, QIU Xue-peng
College Physics. 2022, 41(9): 1. doi:
10.16854/j.cnki.1000-0712.210642
Abstract
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486
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In this paper, we analyze the effect of cohesion energy in solids on the mechanical properties and the lattice dynamics by employing the general equation of cohesion energy U(r)=-Arm+Brn. The dependence of the bulk elastic modulus, force constant, velocity of sound, Debye temperature, melting temperature, and thermal expansion coefficient is given. This work can help students to better understand the relation between the lattice dynamics and the cohesion energy in studies of solid state physics.
On the mathematical fundations of quantum mechanics
YANG Shi-jie
College Physics. 2022, 41(9): 4. doi:
10.16854/j.cnki.1000-0712.210619
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1421
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1080
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In this paper we present a comprehensive description of the mathematical foundations of quantum mechanics. The relevant topics include linear inner product, the completeness of Hilbert space, the functional space and continuous bases representations. We also discuss the self-adjoint operator, the eigen-value problem of the Sturm-Liouville system and the natural boundary conditions. We employ quantum problems as examples to discuss natural boundary condition under the non-regular singularity cases. These conditions are not externally applied but contain in the Schrdinger equation implicitly.
Magnetic field of a finite solenoid—Comments on an approach and corrections to its results
LIN Qiong-gui
College Physics. 2022, 41(9): 9. doi:
10.16854/j.cnki.1000-0712.220059
Abstract
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432
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326
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One approach to the magnetic field of a finite solenoid was published in this journal, which give the results in terms of infinite series. However, the convergence of the series was not examined, thus some divergence issues was overlooked. We reexamine the series and find that it is convergent everywhere outside the cylinder surface (the cylinder surface of the solenoid extended to infinity) but not inside it. The results inside the cylinder surface are recalculated, and the boundary conditions on the cylinder surface are verified.
What is the conductor wire?
LI Zu-bin
College Physics. 2022, 41(9): 15. doi:
10.16854/j.cnki.1000-0712.210591
Abstract
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574
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283
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As a connecting element in circuit，the conductor wire is indispensable but often neglected． This paper discusses the properties of the ideal conductor wire with zero resistance and the actual conductor wire，and explains the contradiction of the deductions from the properties of the ideal conductor wire． We can take the ideal conductor wire as perfect conductor to understand its properties and take the actual conductor wire as resistor to deal with its role in circuit．
Potential algebra of Schrödinger equation with Coulomb potential constraint and supersymmetric spontaneous breaking
WANG Hai-nan, WEN Li, CHEN Jian-lan, XIONG Lu-lin, LUO Guang
College Physics. 2022, 41(9): 17. doi:
10.16854/j.cnki.1000-0712.210625
Abstract
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392
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171
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Supersymmetric quantum mechanics is a very important method in solving the exact solution of Schrödinger's equation. The solution of Schrödinger equation with the Coulomb potential is also a classic problem in quantum mechanics. Based on supersymmetric quantum mechanics, it is also undoubtedly of great significance to study the potential algebra related problems of the stationarySchrödinger equation with Coulomb potential. The potential algebraic correlation problems of the stationary Schrödinger equation with Coulomb potential are studied based on Supersymmetric Quantum Mechanics. First, the shape invariance of partner potential is deduced from the superpotential of radial equation and angular equation, and the eigenvalue and the zero energy ground state wave function of those equations are acquired. Then, the shape invariance is discussed with potential algebraic method. Finally, starting from the radial wave function is not normalizable, we discuss the supersymmetry spontaneous broken.
Lorentz transformation of normalization units in LPIC
LI Meng-chao, LIU Qiao
College Physics. 2022, 41(9): 21. doi:
10.16854/j.cnki.1000-0712.210586
Abstract
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430
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106
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The normalization is related to the incident laser light in laser plasma simulation using PIC method (LPIC).Thus the Lorentz transformation in the program needs to be determined by the incident laser．
Further discussion on two types of infinite integral treated by residue theorem
ZHOU Yun-qing, HUANG Wen-tao
College Physics. 2022, 41(9): 24. doi:
10.16854/j.cnki.1000-0712.220084
Abstract
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645
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288
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Inspired by the article［1］，this paper discusses two kinds of infinite integrals solved by residue the-orem again． Firstly，some characteristics of the two kinds of integrals are analyzed concisely． By combing and sim-plifying the method in the article［1］，the two kinds of integrals are processed with the residue theorem，and the re-sults are obtained when they are greater than 1 and are integers． Then，the two kinds of integrals are recalculated by the method of the residue theorem of multivalued function，the results are obtained when they are greater than 1， and the results are briefly explained． Through the treatment of integral by two methods，we can experience the beau-ty of residue theorem，expand students’vision and enhance their enthusiasm for learning，and lay a good founda-tion for their subsequent courses．
Effect of sample stage height on the determination of lattice constants in XRD experiments
WANG Hong-de, SUN Ying, YUAN Xiu-liang, AN Shi-hai
College Physics. 2022, 41(9): 28. doi:
10.16854/j.cnki.1000-0712.220064
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1146
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375
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X－ray diffraction ( XRD) is an important tool for analyzing the structure of substances and has been paid more and more attention in the teaching of physics － related majors． In this paper，the measurement errors caused by the variation of the sample stage height Δz are systematically analyzed． It is found that the sample stage height shift Δz causes a significant deviation in the diffraction peak position Δ2θ，which in turn causes a deviation in the calculation of the crystal interplanar spacing d and the lattice constant a． The results of the data fitting show that the deviation of Δd /d and the deviation of Δa /a for Si are approximately linear with Δz． Combined with the Bragg－Brentano diffraction geometry，we have theoretically analyzed the above experimental results． This work pro-vides a theoretical basis for the accurate determination of lattice constants in XRD experiments，and will also pro-vide an important reference for the development of related teaching work．
Centennialcommemoration of Mr. Ge ge, an expert of Bohr research
LIU Chao-zhuo
College Physics. 2022, 41(9): 32. doi:
10.16854/j.cnki.1000-0712.220057
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479
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158
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Born on January 22, 1922, Gege studied at Southwest Union University, Peking University, and Tsinghua University successively. In 1953, he entered Beijing Petroleum Institute (today’s China University of Petroleum) where he worked for a whole life. Mr. Ge ge was a famous historian of science, translator, Bohr research expert in China. He translated 12 volumes of Niels Bohr Collected Works independently for 28 years, and was awarded the prestigeous Danish Order of the Dannebrog. He was also proficient in Chinese classical literature and art, such as essay, poetry, seal engraving, calligraphy, painting and other talents. He worked very diligently throughout his life, translating and publishing about 20 million Chinese characters. On the occasion of his centenary birth, the rich achievements in his lifetime were reviewed for the vast number of readers to draw strength.
The exploration and practicing on hybrid teaching in college physics based on problem
WANG Xin , CHEN Shu-guang, XIAO Yan-ping
College Physics. 2022, 41(9): 37. doi:
10.16854/j.cnki.1000-0712.210600
Abstract
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507
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136
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Hybrid teaching (learning) has been widely implemented in universities due to pandemic. However, it remains a challenge for teachers to plan and operate a hybrid class. The article introduces an innovation on designing hybrid physics course in college, which has been proven effective.
Research on the coupled vibrations of Wilberforce pendulum
DENG Xin-Yu, ZHANG Tian-YU, LU Jian-Long, ZHONG Ming, WANG Wei
College Physics. 2022, 41(9): 43. doi:
10.16854/j.cnki.1000-0712.220106
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1030
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473
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Wilberforce pendulum is composed of a vertical spiral string and a pendulum bob fixed on the bottom of the string, it can vibrate vertically and rotate back and forth horizontally. In this paper, the reason why the amplitude of vertical oscillation and horizontal oscillation changes periodical is analyzed experimentally from the perspective of mechanics, and the motion of vertical oscillation and horizontal oscillation of Wilberforce pendulum from the perspective of analytical mechanics. The factors affecting the coupled motion state of Wilberforce pendulum are analyzed, and the experiment is used to study the influence of moment of inertia of Wilberforce pendulum on the coupled motion state. Wilberforce pendulum undergoes three motion states with the increase of moment of inertia: strong coupling, weak coupling and approximate decoupling. control variates are used to study the influence of the initial elongation of the string on the motion of Wilberforce pendulum. The results are in good agreement with the theoretical analysis.
Research on themovement mode of Wilberforce pendulum
WANG Shi-hang, ZHANG Jia-ning, ZHOU Wei, LI Shu-guang, LI Jing, WANG Long
College Physics. 2022, 41(9): 51. doi:
10.16854/j.cnki.1000-0712.220137
Abstract
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533
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183
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In this paper, a mathematical model of the coupled resonance between the up-and-down vibration and torsional swing of the Wilberforce pendulum is established, and its related influencing factors are analyzed. By building an experimental system, the motion mode of the Wilberforce pendulum is observed with the PASCO sensor, and the research is carried out based on the control variable method. The research results show that there is a resonant energy conversion between the up-and-down vibration of the pendulum and the torsional swing, and the rotational inertia of the pendulum will affect the motion state of the pendulum, and it is concluded that the coupling of the two motions leads to the “beat” phenomenon.
Solution of vector on the catastrophe surface of electromagnetism
LIN Tian-zhe
College Physics. 2022, 41(9): 56. doi:
10.16854/j.cnki.1000-0712.220027
Abstract
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369
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372
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In electromagnetism，we often deal with the problem of catastrophe surface of electromagnetic medi-um，which means that the dielectric constant or permeability changes suddenly at the interface． Generally，when dealing with such problems，we will use boundary conditions to deduce the relationship between physical quantities on both sides of the catastrophe surface． On this basis，this paper will repair the existing electromagnetic medium theory，so that the catastrophe surface of electromagnetic medium has a clearer mathematical model，and can accu-rately describe the points on the boundary． This paper is mainly for freshmen who are studying electromagnetism in grade one or grade two． Relevant examples will also be provided at the end of the paper，hoping to help and inspire them to deal with problems in their usual classroom or homework．
COMSOL simulation of ferrite microwave circulator
CAO Xiao, BAI Cui-qin
College Physics. 2022, 41(9): 63. doi:
10.16854/j.cnki.1000-0712.220035
Abstract
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900
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312
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The circulator is a commonly used element in the microwave system, which is capable of selecting the directional propagation of microwaves. Since the microwave element is different from a low frequency centralized parameter element, the students are not easy to form a clear physical image. In this paper, the model of ferrite circulator is established by using COMSOL software. The influence of geometric parameters on the directional guided wave performance of circulator is quantitatively studied by using scattering matrix element (S parameter), and the corresponding geometric parameters when the performance is better are determined; The propagation behavior of microwave in the circulator is intuitively displayed by electric field distribution diagram and energy flow direction diagram. It is very helpful for students to establish the physical image of directional transmission of microwave by circulator.
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