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Table of Content
01 July 2023 Volume 42 Issue 7
Study on the isotropic property of semiconductor conductivity effective mass
XU Jie
College Physics. 2023, 42(7): 1. doi:
10.16854/j.cnki.1000-0712.220570
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504
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In this paper the expression of electron effective mass of semiconductors is deduced when the 3D kspace equienergy surfaces are not spherical by using multivariable calculus and tensor analysis. Then, it is discussed whether the conductivity effective mass tensors of Si and Ge are isotropic. The discussions can promote students′ understanding of energy band structures of semiconductors and its influence on conductivity.
Solution of Schrödinger equation in a 1D homogeneous field
REN Xi-jun, LIU Xiang-rui
College Physics. 2023, 42(7): 3. doi:
10.16854/j.cnki.1000-0712.220552
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578
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The solution of time dependent Schrödinger equation in a one-dimensional homogeneous field is carried out in detail. The idea is, based on the classical trajectory of a classical particle in the homogenous filed, the time dependent wave function can be constructed from this trajectory with a phase factor function which is determined by solving the Schrödinger equation. Guided by this idea, the propagator function of homogeneous field is obtained for both position representation and momentum representation. Meanwhile, Dirac notation for state vectors is employed to obtain the above results for comparison.
Analytical mechanics teaching scheme based on contrastive learning — taking two typical physics problems as examples
WANG Xiao-yun, ZHANG Ji-yuan, LIN Qing-yong
College Physics. 2023, 42(7): 6. doi:
10.16854 /j.cnki.1000-0712.220545
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404
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511
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Aiming at the common problems of students in the teaching of analytical mechanics, this paper starts with two typical physical problems (parachute problem and the double pendulum model), and presents the differences between the two mechanics in dealing with the same physical problem through the form of multi-solution and comparative learning. To guide students' thinking from classical Newtonian mechanics to analytical mechanics, so that they can be integrated into the study of analytical mechanics as soon as possible. At the same time, the appropriate numerical calculation is introduced in the teaching process to further deepen students' understanding of specific physical problems.
The emergent light field of lens without paraxial approximation
XING Rong, LI Ai-hua, GUO Meng-jiao
College Physics. 2023, 42(7): 10. doi:
10.16854/j.cnki.1000-0712.220462
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353
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684
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The equations of emergent light produced by a point object located on the axis of a len are derived without considering paraxial approximation by using a ray-tracing method. Based on the equations, the distribution diagrams of emergent light field are drawn by using Geometric Sketchpad. The results obtained by analyzing the diagrams show that when the len is convex, the energy of the actual emergent light field in the initial range behind the len is mainly distributed in the zone formed by a rotation surface with a special generatrix and a spin axis which is the optical axis. The border of the zone becomes more and more blurred as the distance from the lens increases. On each cross section perpendicular to the optical axis, the actual emergent light field presents three different characteristics successively with the distance from the len increasing. When the len is concave, there is not a zone where the light intensity is greatly stronger than another zones in the emergent light field, and the energy scatters in every cross section.
Skillfully analyzing“virtual short” and “virtual break” for circuit resonance
WANG Wei-gang, TU Zhen-zhen, SHI Xue-jun, LIU Yuan-jian
College Physics. 2023, 42(7): 15. doi:
10.16854 /j.cnki.1000-0712.220420
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389
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As we all know, “virtual short” and “virtual break” are important methods to analyze operational amplifier circuit in analog electronic technology. However, we have found in many years of practice and teaching that this method can also be skillfully applied to the analysis of some resonance problems in the basis of circuit analysis. Moreover, this technique is simple and intuitive, and it can avoid many complicated calculations. So it is convenient and fast to apply. In this paper, the practicability of the proposed method is verified by theoretical analysis and practical examples, and it has much value in related circuit analysis.
The relationship between Fourier transform，Laplace transform and Gabor transform
CAO Zhen-bin
College Physics. 2023, 42(7): 21. doi:
10.16854 /j.cnki.1000-0712.220294
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412
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1002
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As three common integral transforms，Fourier transform，Laplace transform and Gabor transform are of great value both in the theoretical research of mathematical physics and in various engineering applications.In this paper，we take the Fourier transform as the center，and expound the theoretical relationship of the three transforms in detail from the point of view of step-by-step revision.
Talking about the superimposition properties of the Doppler effect
College Physics. 2023, 42(7): 24. doi:
10.16854/j.cnki.1000-0712.220467
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344
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515
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Regarding the superimposition of the Doppler effect, the article “Phase invariance of elastic wave and transformation of plane elastic wave” states that in the case of relativity, the Doppler effect does not have superimposition. This view is not agreed in this article, through clarifying the relationship between the frequency transformation and the Doppler effect, and introducing the definitions of effect factor and superimposition properties, then analyzes this problem by using the phase invariant principle and the four-dimensional wave vector transformation, respectively. The conclusion is that the Doppler effect in the case of relativity is still superimposed.
Optimizing method and quantitatively evaluation on experimental conditions for Frank-Hertz experiment
LI Chao-rui
College Physics. 2023, 42(7): 28. doi:
10.16854/j.cnki.1000-0712.220551
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727
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Frank-Hertz experiment has substantial physics content，and the optimization of its experimental conditions has been extensively discussed in the past.It is a right choice to clearly understand experimental physics by introducing experimental optimizing method and its physical judgment.The preliminary experimental results are obtained by using default parameters provided by equipment manufacturer.On the basis of measurement principles，the collector potential is set to be close to but less than the experimental excitation potential.Then，the filament voltage (current) is appropriately adjusted according to the influence of filament temperature on hot electron emission density.Finally，the first grid potential is changed and its influence is observed.The experimental optimization level is quantitatively evaluated with an indicator defined as the mean and standard deviation of collector current values at the peak and the valley.The accurate experimental results can be obtained on the optimal experiment condition.
Small video production of college physics for new engineering majors and courses
SONG Feng, TIAN Ye, CHEN Ming-jun, HUANG Yi-wei, LIU Quan-yi, HU Han-wen, LI Rui-yu, LIU Li-sa
College Physics. 2023, 42(7): 32. doi:
10.16854/j.cnki.1000-0712.220476
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340
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385
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In recent years, some achievements have been made in the construction of new engineering majors and related courses. As a basic course of new engineering majors, college physics plays an irreplaceable role in cultivating logical thinking and laying a good foundation for mathematics and physics. In order to improve physics teaching effect in new engineering majors and make student deeply understanding physical principles, some small videos were made, which are student-oriented, highlight the characteristics of new engineering major, and pay attention to the integration of patriotic elements and physical principles.
Numerical simulation of tennis racket effect using COMOSL
FENG Rui-qi, BAI Cui-qin
College Physics. 2023, 42(7): 36. doi:
10.16854/j.cnki.1000-0712.220452
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411
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970
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Tennis racket effect (TRE) is a phenomenon that a rigid body’s rotation along its second inertial axis is unstable. As a physical phenomenon observable in everyday life, it is often mentioned in physical teaching.However, quantitative analysis and experiments about it still lack. In this work, a reduced phase space is introduced to give an intuitive explanation of TRE. Numerical simulations of TRE using COMSOL inspected the conditions allowing TRE and identified two modes of TREs. Simulation results of different parameters including initial angular velocities and perturbations are explained by theoretical solutions. To reduce simulation errors, the time duration of a selected portion of the flipping process that is insensitive to perturbations, instead of the complete flipping period, is measured. This method realizes a measurement error of 0.14% in COMSOL simulation. Besides, we carried out an experiment using smartphone, in which two modes of TRE, as well as a linear dependence of the reciprocal of flipping duration to the z component of the initial angular velocity, is observed and matches theoretical predictions. Our work is both beneficial to students’ understanding of TRE in physics teaching and guides the design of teaching experiments considering TRE.
Image intelligent analysis of random phenomenonin gas discharge
LAN Zi-hang, YU Jia-yi, HE Xue-ying, PENG Huai-yu, HE Gui-ming, XU Yu
College Physics. 2023, 42(7): 42. doi:
10.16854/j.cnki.1000-0712.220390
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235
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189
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In this paper, a high-speed camera is used to record the gas discharge information and obtain high-resolution spatial and temporal information. It is found that the discharge pattern is a tree fractal structure, and the fractal dimensions of a single discharge point and multiple discharge points are 1.64 and 1.71, respectively. Through the intelligent contour recognition and centroid marking of a large amount of image information obtained by self-written programs in Python, the location distribution information of discharge points of 5911 images with a time interval of 0.5 ms are obtained. The results show that the location probability of discharge points in space is close to Gaussian distribution, and the time interval distribution of its occurrence is close to exponential distribution.
Measurement of liquid surface tension by lensless Fourier transform digital holography
HONG Ling-er, YANG Ze-bin, ZHENG Jian-yin, PENG Li,
College Physics. 2023, 42(7): 47. doi:
10.16854/j.cnki.1000-0712.220277
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238
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634
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Surface tension is a physical quantity which characterizes the surface properties of liquid. Its measurement has important research significance in the fields of medicine, surface physics and so on. In this paper, a method of digital holography is proposed to realize the non-contact and high-precision measurement of liquid surface tension. Firstly, a lensless Fourier transform digital holographic device based on Mach Zehnder interference light path is built. The hologram taken by CCD is numerically reconstructed by inverse Fourier transform. The phase diagram is obtained by using the phase unwrapping algorithm of Fourier transform, and then the crosssectional profile of static droplets is obtained. The surface tension coefficient of liquid is obtained by fitting the droplet profile with the explicit and accurate solution of Yang-Laplace equation. The relative error of water surface tension coefficient at 20℃ is about 0.42%.
Motion of charged particles in earth’s magnetic field and Mathematica numerical simulation
DONG Shun-cheng, GUO Fang-xia
College Physics. 2023, 42(7): 53. doi:
10.16854/j.cnki.1000-0712.220290
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466
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653
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Based on the single particle orbit model and the geomagnetic field dipole model, and considering the relativistic effect, the sixth-order Runge-Kutta algorithm in the Mathematica software is used to numerically calculate and simulate the trajectories of charged particles moving in the magnetic field in the near-Earth region. The generation of auroras is explained, and the approximation of the guiding center of the charged particles moving in the geomagnetic field is discussed. The results show that: (ⅰ) Observed from the earth’s north pole, the protons captured by the earth’s magnetic field drift in the clockwise direction, and the electrons in the anticlockwise direction; (ⅱ) The numerical simulation results of the motion period of each particle motion are in good agreement with the theoretical values in the literature; (ⅲ) When the throwing angle of the incident particle from (4Re,0,0) is less than 7.38°, the charged particle will collide with the atmosphere on the earth’s surface and sink, and there is the possibility of producing auroras. When it is greater than 7.38°, the particles will be bound in the geomagnetic field, forming a radiation belt; (ⅳ) When other conditions are the same, the farther the charged particle throwing point is from the earth, the greater the drift velocity; the greater the throwing angle, the greater the Its drift speed is also greater; (ⅴ) For particles with low energy, the guided center trajectory can well represent the actual trajectory of particles in the first-order approximation.
Charge distribution of two charged conductor spheres at equal potential
WU Zhi-yong, CAO Xiu-feng
College Physics. 2023, 42(7): 61. doi:
10.16854/j.cnki.1000-0712.220454
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491
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In this paper, the charge distribution of two charged conductor spheres at equal potential is solved by multiple image method. We mainly focus on the charge quantity distribution and the average surface charge density distribution as function of the radius and spacing of the two spheres. By choosing suitable coordinates, this paper gives the general formula of n-order mirror charge’s charge quantity and position, and the analytical expression of total charge quantity, when two conductor spheres are in contact. It is found that when two conductor spheres are in direct contact, the charge of the two spheres can be solved strictly, and the expression of the ratio of charge of the two spheres is given. As the distance between two equally potential conductor spheres increases, the ratio of the charges tends to the ratio of the radius. Considering the limiting case where the radius of one of the conductor spheres tends to 0, we find that the charge ratio of the small sphere to the large sphere tends to 0, and the ratio of the average surface charge density tends to infinity when the two spheres are not in direct contact, but tends to π2/6 when the two spheres are in direct contact.
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