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Table of Content
20 April 2022 Volume 41 Issue 4
Proof of non-degeneracy theorem for one-dimensional bound states
GAO Si-jie
College Physics. 2022, 41(4): 1. doi:
10.16854/j.cnki.1000-0712.210493
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We discuss the non-degeneracy theorem for one-dimensional bound state, pointing out that the proof of this theorem in typical textbooks only applies to wave functions without zero point. For wave functions vanishing at some points, we analyze the behavior of the function near those points and prove that the theorem still holds.
Study and discussion on two confusing points in teaching of crystal structure
YANG Jun
College Physics. 2022, 41(4): 2. doi:
10.16854/j.cnki.1000-0712.210346
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662
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145
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Two confusing points in teaching of crystal and on many current textbooks are concerned. Lattice transformation is used to infer whether the formation being a new Bravais lattices or not and additional constraint is added to four indices. The lattice transformation must be carried out in same crystal system, and the transformation into another crystal system could not deny the original lattice. Three methods are provided to prove that the additional constraint in four indices has a rigorous mathematical foundation. This is favorable for students to understand the related contents in crystal structures.
How to uniformly describe the transmission model of light in the course of electrodynamics
CHEN Pei-feng
College Physics. 2022, 41(4): 7. doi:
10.16854/j.cnki.1000-0712.210396
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612
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334
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Combined with the characteristics of Optoelectronic Information Science and engineering specialty and taking the derivation of “light” and “Gaussian beam” as an example, this paper explores the teaching of the internal relationship of the theoretical model of light transmission in free space. Practice has proved that this method is very necessary for students to understand the follow-up courses on light transmission, and provides a certain reference for the teaching of basic theory courses of engineering specialty.
Physical interpretation of quantum Zeno effect
YANG Zhao-hui
College Physics. 2022, 41(4): 11. doi:
10.16854/j.cnki.1000-0712.210482
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895
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Starting from basic laws of quantum mechanics, this paper attempts to analyze and discuss the quantum Zeno effect of quantum measurement problems. Combined with some classical experiments and explanations of some schools, this paper focuses on the dynamic decoherence model and makes a physical interpretation of its own.
The moments of inertia of elliptical rings and elliptical plates in polar coordinates
LI Lei, CAI Yue, LI Wenjun, LIU Tingting, WAN Huijun
College Physics. 2022, 41(4): 14. doi:
10.16854/j.cnki.1000-0712.210273
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1054
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In this work, the moments of inertia JF (JO) about an axis through its foci (centroid) and perpendicular to the plane of the elliptical ring and elliptical plate are calculated in polar coordinates. Furthermore, the dependence of moment of inertia JF (JO) on eccentricity e for elliptical ring and elliptical plate is also studied.
The exterior magnetic spherical multipole expansion
YU Tian, LIN Fang, YAO Xin, QI Jian-qi, ZHANG Zhi-you, NIE Ya, WANG Lei, ZHU Jian-hua
College Physics. 2022, 41(4): 17. doi:
10.16854/j.cnki.1000-0712.210266
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In this paper, the exterior magnetic spherical multipole expansion is discussed, including the expansion of magnetic scalar potential and the expansion of magnetic vector potential. Two different approaches are explored to derive the exterior magnetic spherical multipole expansion of magnetic vector potential. One is based on the exterior magnetic spherical multipole expansion of magnetic scalar potential, the other one starts from the expression of the magnetic vector potential and takes advantage of its Debye potential representation to directly obtain the expression.
A new method for measuring liquid refractive index by analyzing a defocused image of liquid-core cylindrical lens
WANG Yan, WANG Rui-xian, ZHAO Qing-hao, MENG Wei-dong, PU Xiao-yun
College Physics. 2022, 41(4): 21. doi:
10.16854/j.cnki.1000-0712.210313
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713
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In this paper, a new method for measuring liquid refractive index based on a spherical aberration-free liquid-core cylindrical lens is presented by analyzing an experimental defocused image on the focal plane. A spherical aberration-free liquid-core cylindrical lens is designed and fabricated which has small spherical aberration and accurate imaging in a wide range of refractive index. Using the designed lens, according to the relationship between the experimental image and the liquid refractive index, only one defocused image is needed to measure the liquid refractive index. The method is used to measure the refractive indexes of 21 groups mixed solution at room temperature (20℃). The measured results are in well agreement with those using Abbe refractometer. The defocused images simulated by ZEMAX and ray tracing method are consistent with the experimental results. The experimental and simulation results show that the method has the characteristics of simple system, good stability, simple operation and fast measurement speed.
Teaching practice based on knowledge grouping
College Physics. 2022, 41(4): 27. doi:
10.16854/j.cnki.1000-0712.210418
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589
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In view of the uneven physics foundation of college students, teaching reform according to knowledge grouping has been carried out, including increasing class time for poor basic classes. The practice lasting for more than two years has shown that this reform program has obtained obvious effect.
Construction and implement of blended teaching model in specialized basic courses under the background of new engineering
ZHANG Jian-ping
College Physics. 2022, 41(4): 32. doi:
10.16854/j.cnki.1000-0712.210309
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772
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388
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The blended teaching model in specialized basic courses has been widely used in recent years under the background of “internet +” and new engineering. However, the online bad interactivity and offline low participation significantly influenced on its sustainable development. In this work, the learning pyramid theory, information processing theory, and cognitive load theory are analyzed to reveal the main constraint of average retention rate of learning, learning initiative and cognitive load, and to propose the measures of improving students learning quality. “4+3+1” online and offline blended teaching model of specialized basic courses for engineering students is suggested according to CDIO educational ideas and OBE teaching mode. The teaching contents, teaching methods, teaching implementation and teaching evaluation are structured. Then, they are applied in course of Fundementals of Thermal and Fluid Mechanics. The practice showed that 92% of students thought that this blended teaching model could improve their learning initiative and help them to effectively control their learning process. At the same time, it also may help students to develop a good habit and attitude of learning, gain a sense of achievement, and enhance self-confidence in order to improve the average retention rate of learning. This research provides also a reference for theory teaching in specialized basic courses.
Ideological and political teaching design and practice in mechanics course ——Taking “preliminary fluid mechanics” as an example
PENG Zheng, PAN Jiang-ling, WU Di
College Physics. 2022, 41(4): 39. doi:
10.16854 /j.cnki.1000-0712.210338
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As a classic scientific paradigm, physics has natural advantages in ideological and political education for carrying forward the spirit of science and shaping value orientation. Mechanics, as the first successful example in physics, is the knowledge that students have the most exposure to. Therefore, the reasonable designed ideological and political points in mechanics curriculum can most arouse students
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interest and resonance, help students build up correct outlook on the world, the life and the value, and also establish morality. Design ideas for introducing ideological and political elements into the mechanics course is illustrated by taking the content of preliminary fluid mechanics as an example. Detailed design and practice process of this course are introduced and the teaching effect is summarized.
Exploration ofideological and political education in space-time view of special relativity
LIU Shu-jing, CHU Xin-wei, LUO Ming-yan, JI Qiang, JU Dan-dan, LIU Jun-yu, WANG Da-shen, XIE Ming-nian
College Physics. 2022, 41(4): 44.
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In this paper, the space-time view of special relativity is taken as an example, and some specific proposals of implementing curriculum ideological and political education are promoted. The ideological and political elements are distilled from the knowledge of spacetime view of special relativity and put into teaching by using appropriate implementation strategies and samples. Therefore, correct value pursuit and ideal belief can be conveyed to students gradually, which can perfect the personality and promote the thinking and political quality of college students. Finally, the teaching and educational effect is evaluated by means of questionnaires, which can improve teachers
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self-ability for presenting curriculum ideological and political education. Hence in the curriculum ideological and political education based on special relativity, all function modules of whole teaching processes are obtained, which includes preparing the lesson, teaching, learning and evaluating. The curriculum ideological and political education is deserved a long-term research and perfect subject. It is hoped that this teaching research can provide a mentality and play a role for improving the curriculum ideological and political education.
Influence of Magnus force on the trajectory of balls
HUANG Ming-xuan, LU Ai-jiang
College Physics. 2022, 41(4): 52. doi:
10.16854 /j.cnki.1000-0712.210248
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781
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Magnus effect describes that，the difference of fluid velocity in the vicinity caused by the rotation of objects in viscous fluid,leads to a transverse Magnus force.It is in the vertical direction of plane composed of angular velocity vector and translational velocity vector.Magnus force is an important factor to influence the trajectory of projectile,and it is often the reason for forming various “curve ball” in ball games.Taking football and table tennis as examples,this paper analyzes their forces,numerically solves their motion equations,compares the trajectory and motion characteristics of small balls under different angular velocities.It systematically studies the influence of Magnus force produced by different angular velocities on the trajectory of small balls,and analyzes the physical principles of several skilled movements in football and table tennis.
Home-based experiments of sound velocity varying with the temperature in air
LUO Jing, GUO Zhong-hua
College Physics. 2022, 41(4): 56. doi:
10.16854/j.cnki.1000-0712. 210211
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1336
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443
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The sound velocity in air varies with temperature. In this paper a finite length straight pipe is used to measure the sound velocity, and mobile APP is adopted as a transmitter and a receiver of sound wave. A constant temperature condition is fulfilled in the internal area of the pipe in order to accomplish the sound velocity measurements at different temperature by standing wave method. The relative errors of the measurements maintained to be less than 2%. This home-based experiment proposed in this paper is a prolongation of traditional physical experiments. It can be arranged as an online experiment during special epidemic period. It can also promote the comprehensive quality and the practical innovation abilities of students.
Derivation of speed scaling factor in molecular dynamics method
QI Nan, WANG Sheng-jun
College Physics. 2022, 41(4): 61. doi:
10.16854/j.cnki.1000-0712.210204
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744
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422
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In the case of using the molecular dynamics method to simulate the micro-canonical ensemble, taking the monoatomic particle system as an example, the mathematical expression of the scaling factor under the International System of Units is given. Then it explains how to rescale the physical quantity to obtain the dimensionless formula, which makes the calculation more convenient in the simulation. The physical meaning of the time unit in the dimensionless operation is given. Finally, the mathematical expressions commonly used in textbooks for the speed scaling factor of the balance process are derived.
Numerical simulation of one-dimensional unsteady hydrodynamics
FU Zhi-hao, YU Cong
College Physics. 2022, 41(4): 65. doi:
10.16854 /j.cnki.1000-0712.210199
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686
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715
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The discontinuous shock wave solution in nonlinear partial differential equations of fluids is a very challenging problem in physics.The Riemann problem can be solved theoretically by analytical method，but the approximate solution method can also be used to track and capture the shock waves effectively in the numerical simulation of fluid dynamics.In this paper，a one-dimensional shock tube is taken as an example，adopting the Roe flux difference splitting scheme to the basic equations of fluid and numerically simulated.It is found that the method is in good agreement with theoretical solution.
Instrument for measuring the liquid viscosity coefficient based on under-damping vibration
TAN Chang, ZHANG Guo-xing, LU Pan-gong, GAO Jian-fei, SHENG An-di, MENG Gao-qing
College Physics. 2022, 41(4): 71. doi:
10.16854 /j.cnki.1000-0712.210486
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582
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328
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In this paper，a damping vibration device for measuring the viscosity coefficient of liquid is designed.A spring vibrator is taken as the core，and a photoelectric proximity switch is used to collect data.A digital oscilloscope is employed to display the image and transmit the image data to computer for analysis.This method has a wide range of application，is convenient for collecting and analyzing experimental data.It also avoids various interference factors in the experiment and eliminated the disadvantages of traditional fallingsphere method.It also improves the accuracy of experimental measurement.
Calculation of states density in solid state physics
DU Lin, TIAN Hong-yu, REN Chong-dan
College Physics. 2022, 41(4): 77. doi:
10.16854 /j.cnki.1000-0712.210438
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2795
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The electronic density of states is the number of states in the unit energy range.It is a physical quantity closely related to electronic energy band structure.In order to calculate the specific heat of electrons and the transport properties of crystals,a more accurate method must be used to calculate the electronic density of states.The processing of this in general textbooks usually adopts simplified models,which does not reflect the calculation ideas of states density in general.In this article,two-dimensional graphene and three-dimensional face-centered cubic lattice are explained in detail based on the formula of electronic density of states.The calculation steps of the density and a detailed explanation based on numerical calculation are given.
The magnetic field of a uniformly magnetized permanent magnetic bar
CHEN Yi-han, ZHANG Yi-wen, ZHANG Yan-fang, HUANG Fei
College Physics. 2022, 41(4): 81. doi:
10.16854 /j.cnki.1000-0712.210462
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In this paper，the magnetic field distribution along the axis of a finite permanent magnetic cylinder uniformly magnetized in its axial，diametrical and arbitrary directions，and the magnetic field distribution in the whole space of an infinite permanent magnetic cylinder uniformly magnetized in its axial，diametrical and arbitrary directions have been systematically calculated in the view of molecular current and magnetic charge.
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