College Physics

The effect of quantity momentum in modern quantum physics

WANG Hai-jun

College Physics. 2023, 42(6): 1. doi:10.16854/j.cnki.1000-0712.220463

Abstract ( 636 )

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Nowadays the public's familiarity with classical momentum is almost as good as energy. The law of conservation of momentum is deeply rooted in the hearts of the people. The center collision effect of equal-mass balls is even used in entertainment programs and dances. This article demonstrates the application of quantum momentum by estimating several typical physical examples in quantum theory, leading readers to reveal the nature of momentum step by step, and also enable readers to deeply understand the physics of wave functions in quantum mechanics.

Discussion on self-reproducing modes in stable and unstable laser resonators

LI Min

College Physics. 2023, 42(6): 6. doi:10.16854/j.cnki.1000-0712.220286

Abstract ( 506 )

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In this paper, the analytical expressions of selfreproducing modes in general stable and unstable spherical mirror resonators are derived by Fresnel-Kirchhoff diffraction integral method. The law of self-reproducing modes changing from stable resonator to unstable resonator is revealed. Furthermore, the self-reproducing mode in the unstable resonator is also obtained under the condition of geometric optics approximation. By comparing with the diffraction integral results, it is found that the spatial distributions of the lowest-order even symmetric mode (i.e., fundamental mode) and the lowest-order odd symmetric mode of the unstable resonator obtained based on geometric optics approximation are consistent with the diffraction integral results. For higher-order self-reproducing modes, when the unstable resonator is close to the stable resonator, there is a large difference between the results from the geometric optics approximation and the diffraction integral. The results in this paper can be used as an important supplement to the teaching content of laser principle.

Teaching practice of two-dimensional material physics

LIU Bing-lin, YUAN Xiang

College Physics. 2023, 42(6): 12. doi:10.16854/j.cnki.1000-0712.220348

Abstract ( 330 )

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Two-dimensional materials such as graphene present novel properties because the charge and heat transport are confined to a two-dimensional plane, which attracts intense research interests. The course teaching and scientific research of two-dimensional materials was integrated in the course of physics and device application of two-dimensional materials. It is introduced that the development of two-dimensional materials especially the recent progress, so that the history and development of two-dimensional materials are clearly introduced, and the overall course is understandable for undergraduates. In addition to the theoretical part, a series of lab experiments are added, such as the exfoliation of two-dimensional materials, Raman spectrum characterization, and fabrication of field effect transistor. By combining the two-dimensional physics theory and in-course experiments, it helps to increase students' perceptual understanding of theoretical knowledge and establishes the correct physical picture.

Does quantum mechanical analogy of quasi-normal modes in black hole physics exist?

HE Xiao-kai, CAO Zhou-jian

College Physics. 2023, 42(6): 17. doi:10.16854 /j.cnki.1000-0712.220395

Abstract ( 297 )

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With the breakthrough research progress of gravitational wave detection and telescope observation of black hole event horizon, the quasi-normal mode of black hole has caused a new round of research upsurge. The quasi-normal mode of black hole is described as the eigenfunction of time independent Schrodinger equation with complex frequency by many literatures. Such description leads readers to a misunderstanding that the concept of quasi-normal mode comes from the Schrodinger equation, or quantum mechanics. The current paper will analyze this issue and point out that there is no quantum mechanical analogous to the quasi-normal mode of black hole. We clarify the relevant physical concepts and point out that quasi-normal modes are the physical behavior of wave equations admitting dissipation characteristics.

One-dimensional potential scattering of th(λx)

YANG Wei

College Physics. 2023, 42(6): 21. doi:10.16854/j.cnki.1000-0712.220322

Abstract ( 407 )

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The scattering problem in quantum mechanics has always been a difficult point of study and the basis of theoretical research. The purpose of this paper is to provide an exact solvable example for understanding scattering. We obtain the exact solution of one-dimensional time-independent Schrodinger equation with th(λx) potential, basis on this exact solution, and using the asymptotic expansion property of hypergeometric function, the corresponding reflection and transmission coefficients are calculated. At the same time, it is also found that when the constant λ approaching to infinite limit, the reflection and transmission coefficients of th(λx) potential and the step function potential are exactly equal to each other.

Gauge transformation of electromagnetic fields in two ideal media

SUN Yu-ming

College Physics. 2023, 42(6): 24. doi:10.16854/j.cnki.1000-0712.220303

Abstract ( 368 )

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In gauge field theory, gauge invariant quantities are endowed with physical meaning, while gauge dependent quantities are regarded as redundant mathematical objects. In that case, why are gauges still widely used in modern physics? Based on the analysis of some specific gauge fields, Rovelli gives an explanation that the coupling between gauge fields needs to be described by gauge dependent quantities. Electromagnetic field is the simplest gauge one, and the Lagrangian of free field can be described by gauge invariant relative generalized coordinates. The interaction between the electromagnetic fields of two ideal media at the interface can be expressed by the relative generalized coordinate difference of the two fields. In order to preserve the gauge invariance of this action, the gauge functions of the two fields must be time independent and their gradients are equal．

Further exploration on time dilation effect

ZHANG Yue-xia, ZHANG Xiao-long

College Physics. 2023, 42(6): 28. doi:10.16854 /j.cnki.1000-0712.220243

Abstract ( 504 )

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The conclusion of time dilation effect is obtained usually through an example in special case in the textbook.In order to deeply explore whether the time dilation effect is still corrected under general conditions，this paper expounds the universality of time dilation effect by changing the position of the mirror and the optical path.We hope it can provide a reference for teachers and students studying special relativity，and understand deeply of the time dilation effect.

Theoretical and experimental study of transverse vibration of string, beam and ring

FANG Yi-zhong, CUI Xin-tu, SHEN Han, HUANG Zhen-cheng, FENG Rao-hui, LIAO De-ju, PANG Xiao-ning

College Physics. 2023, 42(6): 32. doi:10.16854/j.cnki.1000-0712.220466

Abstract ( 526 )

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From the strict derivation of transverse vibration of string, the explicit solution of wave velocity is obtained. Through measuring the wavelength and eigen frequency of resonance, the experiment value of wave velocity is also obtained, which is well agreed with the theoretical value. The transverse vibration equation of beam is also solved exactly. The simulation of the problem which one end is clamped and the other is free, is performed. The expressions of first several resonant eigen frequencies and the sites of standing-wave nodes are obtained so as to get the general solution. Further, the fundamental frequencies and resonant frequencies of the previous order overtone of steel slender strips under different lengths are measured. The co-ordinates of standing-wave nodes are observed and equivalent to the theoretical results, and the Young’s modulus of the strips are calculated, which are well corresponded with standard values. Furthermore, the case of small radial vibration of ring is popularized. The resonant frequencies and wavelengths are also measured, and the elastic modulus of circular cross section ring are obtained, where are also accorded with the existing values.

Using Helmholtz resonators to measure sound velocity based on smartphone

ZHAI Li-peng, CHENG Lin, ZHANG Jun-wu, CHANG Kai-ge, TONG Tong

College Physics. 2023, 42(6): 40. doi:10.16854/j.cnki.1000-0712.220247

Abstract ( 426 )

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The Helmholtz resonance principle is delved in detail. A sound velocity measurement experiment is designed that may be done outside a laboratory setting. The measurement results are verified by using two data processing methods, arithmetic average and data fitting. The relative errors are 3.0 percent and 2.8 percent, respectively. The experiment equipment is readily available in everyday life and can be utilized by students for autonomous experiment projects at home or outside classroom.

Practice and exploration of a new mode of physical practice course

XIA Ming-gang, ZHANG Sheng-li, ZHANG Lei, HUANG Li-qing, YANG Sheng-chun, LIU Jie

College Physics. 2023, 42(6): 46. doi:10.16854/j.cnki.1000-0712.220433

Abstract ( 391 )

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A new practical teaching mode which is different from the past is put forward in this paper. The teaching is carried out from the aspects of searching for information, participating in teaching, discussion, designing experiments and summarizing cutting-edge scientific problems by students, so that they can learn actively and become the leader of learning. The assessment is also composed of above parts in which students also participate. This practice teaching mode can realize online practice teaching. On the one hand, this practical teaching connects theory and practice closely through frontier scientific problems and practical knowledge. On the other hand, through the full participation of students, it can promote their autonomous learning, improves their interest in learning, and stimulates their learning motivation.

An experimental design of two-dimentional Doppler effect based on beat frequency measurement

ZHENG Wen, QIU Lei, XIE Zheng-qing, LI Hong-tao

College Physics. 2023, 42(6): 52. doi:10.16854/j.cnki.1000-0712.220271

Abstract ( 327 )

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Most of traditional Doppler effect experimental devices used in college physics experiments are one dimensional. In this paper, by applying beat frequency and circular motion, a two-dimensional Doppler effect experimental device is designed and produced, which let sound wave listened and make a quantitative study on Doppler effect shift. The device has two sound sources of the same frequency (the measured sound source and the reference sound source). Due to make a uniform circular motion, the frequency-frequency sound wave emitted by the measured sound source and the reference one meet and superimpose to form an audible beat sound, which is converted by the radio device into an electrical signal and then accepted by an oscilloscope to form a beat image. It makes the Doppler effect audible and visible. This experimental device expands the experimental teaching contents of studying Doppler effect, features novel scheme and optimization of traditional experiment, and has certain practical value in experimental teaching.

A low-cost demonstration of linear paul trap

JIANG Wen-yang, ZHAO Yi-wei, BAI Zai-qiao, WANG Ai-ji

College Physics. 2023, 42(6): 57. doi:10.16854/j.cnki.1000-0712.220302

Abstract ( 329 )

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In this paper a low-cost linear Paul trap demonstration device is introduced. Using a neon lamp transformer as high voltage power supply and four stainless steel cylinders as electrodes, an alternating quadrupole electric field can be obtained. When charged sporangium powder is sprayed into the region surrounded by the electrodes, sporangium with suitable charge can be captured by alternating electric field. Illuminated by a laser beam, localized trajectories of the captured particles can be clearly observed. The electric potential distribution of Paul trap is numerically calculated by using a simplified electric potential model in Matlab, and the particle trajectory is simulated by analyzing the gravity, electric field force and air resistance of the particle. The charge of the particles is also estimated.

Optical research on relative paper-making time based on Phyphox

YAN Yun-bo, WU Xiang, LI Fu-cheng, ZHAO Yu-tong, XIE Yun-tian

College Physics. 2023, 42(6): 61. doi:10.16854/j.cnki.1000-0712.220255

Abstract ( 378 )

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In this paper, three smart phones and a self-made cassette are used to perform an optical determination of the relative time of paper production. Based on different cellulose content in the same paper of different ages, the glucose concentration of the solution is different after hydrolysis, which in turn leads to different ways of acting on light (absorbance) after color development. The color of the sample hydroxylation is processed and a new double-layer glass slide model is adopted, which made up for the shortcomings of traditional experiments in offsetting the reflected light. Three smart phones are used as the light source end, the detection end and the control end, respectively. Among them, the detection end is based on the Phyphox software to detect the changes of the incident light intensity and the transmitted light intensity with time, and processes the data through the Lambert-Beer law to obtain the functional relationship between the absorbance and the age of the paper. Taking the People's Daily on January 10, 2017 as the paper to be tested, the detected value is 2017.163. Comparing the detected value with the real value proves the reliability of the Lambert-Beer law and the feasibility of the self-made experimental device.

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