College Physics

Velocity operator and Zitterbewegung of electron

KA Xing-lin

College Physics. 2019, 38(12): 8.

Abstract ( 908 )

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The concepts of velocity operator and Zitterbewegung in some foreign textbooks in quantum mechanics are criticized and the origin thereof is analyzed.

Some notes on the motion of a charged particle in the field of a magnetic monopole

LIN Qiong-gui

College Physics. 2019, 38(12): 10. doi:10.16854 /j.cnki.1000-0712.190055

Abstract ( 1064 )

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We point out that the simplified calculations in the textbook on the scattering of charged particles by the field of a magnetic monopole and the quantization of electric charge lead to some obvious error. Reexamination of the orbit of the charged particle yields the physical picture: the azimuthal angle as well as the polar angle θ of the incident particle change after scattering. In particular，for very large impact parameter，the change of is approximately ±π/2. The change of the angular momentum is calculated and reasonable results are obtained. The scattering cross section is also discussed.

A brief probe: time evolution of quantum state based on Schodinger equation

SONG Jie, WANG Xiao-ou, HUO Lei, ZHANG Yu, ZHAO Yuan

College Physics. 2019, 38(12): 15. doi:10.16854 /j.cnki.1000-0712.190075

Abstract ( 1536 )

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In the teaching of quantum mechanics，Schrodinger equation is the core part of describing the evolution of a quantum system. Research on Schrodinger equation enables students to understand the differences between quantum physics and classical physics. In the course of quantum physics，Schrodinger equation is very important for students to have a grasp of the properties of quantum state. However，in teaching，most examples focus on the stationary Schrodinger equation. The students cannot master the time evolution of quantum state very well. Thus we introduce the simplest system which is composed of a single photon and coupled cavity system. The probability of photon in different cavities varies with time. Simultaneously，the simplest Hamiltonian is used to describe the hopping process of photons in the system.The analytical expression of the probability depending on time is given.As a result， the time evolution of quantum state can be understood more intuitively.

Notes on exact solutions for ( 2+1) -dimensional dispersive long wave equation

LIU Chun-ping, ZHANG Qun-ying

College Physics. 2019, 38(12): 18. doi:10.16854 /j.cnki.1000 0712.190036

Abstract ( 712 )

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Further study on the exact solutions for ( 2+1) -dimensional dispersive long wave equation has been done. Firstly，we show that the solutions obtained by the extended F /G-expansion method are equivalent to the solutions obtained by the extended tanh-expansion method. Then，through a transformation and the modified homogeneous balance method，the more exact solutions for ( 2+1) -dimensional dissipative long wave equation are given.

Study of the problems of particles falling along the fastest down line and two connected line segments with fixed ends

SHAO Yun

College Physics. 2019, 38(12): 20. doi:10.16854 /j.cnki.1000-0712.190071

Abstract ( 1215 )

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Although there are many articles about the origin principle of the brachistochrone ( i. e.，the cycloid) at present，most of them directly apply the law of optical refraction to analogical reasoning，lacking of detailed introduction to the source of method and discussion on the details of motion，or just do local numerical calculations and lack of physical connotation. As for the more basic problem associated with the cycloid that the time when the particle falls along two connected straight lines fixed at the beginning and end，few papers have been written to study it. This paper first derives the " refraction law" in the problem of prompt drop of particle，and then uses it to deduce the equation of the brachistochrone ( i.e. the cycloid) . It is proved that the dropping motion of a particle along a cycloid is equivalent to the absolute motion of the corresponding point on a uniform rolling circle. The equation of the steepest descent motion and the methods of calculating the specific parameters of the cycloid and the descent time of the particle are given，and some examples are given to illustrate them. It is pointed out that there are different formulas for calculating the parameters of cycloid when the landing end is at the left and right half arch of the cycloid. It is simply proved that the cycloid is only shortcut. Finally，through the method of finding extremum， the position of the fastest descending break point of two connected straight lines with fixed ends，and the positions of the fastest descending break points with given longitudinal or abscissa coordinates are calculated. Through listing and drawing，the change rule of landing time with breaking point is analyzed.

Light ray，wave and photon as well as model of light in optics

LI Jun-gang, HU Hai-yun

College Physics. 2019, 38(12): 28. doi:10.16854 /j.cnki.1000 0712.190158

Abstract ( 2322 )

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Light ray，wave and photon are different physical models in different stages of the development of optics. These models have different application ranges due to their different backgrounds. The applicable conditions of these models are clarified in order to deepen the students’understanding of the corresponding physical concepts and laws.

Measurement of the young’s modulus of metal wires based on the dial gauge

XU Cheng-lin, ZHANG Yuan-di, FAN Ze-bin

College Physics. 2019, 38(12): 33. doi:10.16854 /j.cnki.1000-0712.190173

Abstract ( 1523 )

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A method of measuring young’s modulus of metal wires with dial gauge is introduced in this paper. Aiming at the deficiency of the common method to measure young’s modulus of metal wires，this method proposes to use a micrometer instead of the optical lever device to measure the tiny elongation of metal wires when it is stretched. Experimental research and analysis reveal that the accuracy of the tiny elongation of three different wire materials measured with a micrometer can be improved by three orders of magnitude compared with that obtained by the common optical lever method. Two less physical quantities need to be measured，and the measurement accuracy of young’s modulus is improved by an order of magnitude. At the same time，this method has the advantages of simple device，rapid measurement and accurate results.

Principle of hand-operated electrostatic induction motor

LU Jun-ling, GU Chen, QIN Lian-hua, REN Nai-jing, MA Bo-yi

College Physics. 2019, 38(12): 36. doi:10.1685 /j.cnki.1000-0712.180703

Abstract ( 5915 )

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Hand-operated electrostatic induction motor is a charge amplifier with positive feedback when the handle moves clockwise. If there is a certain initial charge on the capacitor of Leighton bottle，the electrostatic induction will appear on the metal brush generated by the charge on the exposed part of the capacitor electrode，and the positive and negative charges will appear at both ends of the brush. When the insulation turntable rotates，the conductor foil on it will carry net charges after sliding through the metal brush. When conductor foils meet collector forks connected to the capacitor electrodes of the Leighton bottle separately， the Leighton bottle is charged by the tip discharge，and the charge in the Leighton bottle is increasing.

Innovative research on college physics experiment teaching based on wechat combined with H5 technology

BAI Liang, MA Cheng-ju

College Physics. 2019, 38(12): 40. doi:10.16854 /j.cnki.1000-0712.180590

Abstract ( 1266 )

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By using wechat public account as a platform and combing H5 technology，an innovative design for the teaching content of college physics experiment is carried out. This paper introduces a learning process including both online and classroom and also gives the idea and effect of online learning and the importance of teachers’ participation and guidance in autonomous online learning. Finally，according to the feedback of the students’online learning and the mutual complementation of the classroom teaching content，a new method and technology for improving the teaching content of physics experiment and teaching quality is proposed.

Research on the Lissajous figures using azimuthal-radial pendulum

ZHOU Yu-han, LIANG Han-pu, LI Chuan-nan, SHI Li-wei

College Physics. 2019, 38(12): 44. doi:10.16854 /j.cnki.1000-0712.190168

Abstract ( 1449 )

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By analyzing the elastic rod of radial pendulum and the natural vibration frequency of the azimuthal-radial pendulum，the pendulum Lissajous figure is studied by using the method of camera exposure. We analyze the effects of some parameters including the length of the cycloid，the initial release angle and the quality of the pendulum on the trajectory of the pendulum. It is found that the experimental results consistent well with the theoretical predictions.

Research on characteristics of gyroscopic precession

QIAN An-na, LIU Jia-yi, ZHOU Jin-hao, CHEN Xing-jie, BAO Ri-ma

College Physics. 2019, 38(12): 48. doi:10.16854 /j.cnki.1000-0712.190061

Abstract ( 1783 )

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In this paper，an experimental scheme to study gyroscope precession characteristics is introduced. Based on the principle of gyroscope precession，the relationship between the angular velocity and the angular velocity of the gyroscope precession is derived，and the gyroscope experimental device is fabricated based on the principle of electromagnetic induction and the characteristics of the photoresistor. At the same time，the revolution period and rotation period of the gyroscope are accurately measured，and the calculation is further calculated for the rotational inertia of the gyroscope，the calculation results obtained by the parallel axis theorem verify the correctness of the theoretical method and measurement results of the device.

Research on the jumping coin placed on cooled bottle neck

QING Bing-cheng, LIU Ping, YUAN Shi-bo, KONG Chun-cai, Fang Ai-ping, TIAN Peng-bo, LI Hong-rong, GAO Hong, WANG Xiao-li

College Physics. 2019, 38(12): 52. doi:10.16854 /j.cnki.1000-0712.190167

Abstract ( 1129 )

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In this paper，we study the phenomenon that the coin placed on a cooled bottle neck will jump for several times when placing them in a relatively high temperature. The zero-dimensional transient heat transferring equation is used to describe the change of air temperature in the bottle. The condition for the jumping of coin is obtained from the force moment analysis. And MATLAB numerical simulation is used to study the change of air pressure in bottle and period of jumping. Then，the effects of the phenomenon are studied through different kinds of bottles and of coins，which obtain the same results as the theoretical analysis.

A range finder based on the Biot-Savart law

LI Pei-jiang, ZHOU Ai-ping, NIE Yun-hao, LI Tai-fu, YAN Wei-lu

College Physics. 2019, 38(12): 57. doi:10.16854 /j.cnki.1000-0712.190025

Abstract ( 1111 )

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According to the Biot -Savart law， the theoretical basis of the distance measured by the magnetic field of loop coils is proposed，and a range finder based on the magnetic field of loop coils is designed and made.The experimental results have about error within 5% when the measuring distance is in the range of 15 ～ 40 cm，which can basically achieve the design effect.

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