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Table of Content
20 October 2018 Volume 37 Issue 10
An unified approach to derive the Fokker-Planck equation for distribution functions of three types in quantum phase space
XU Ye-jun1，DING Xiu-chun1，HE Rui2
College Physics. 2018, 37(10): 1-3. doi:
10.16854 /j.cnki.1000-0712.180070
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1629
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A new set of differential relationship of operators are obtained by normally and anti-normally ordering the generalized Wigner operator with s parameter，and then an unified method is proposed to derive the Fokker-Planck equations for distribution functions of three types in quantum phase space.
A new method for re-ordering of the coordinate and momentum operator functions
YANG Yang1，FAN Hong-yi2
College Physics. 2018, 37(10): 4-6. doi:
10.16854 /j.cnki.1000-0712.180231
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2053
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690
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Because the coordinate and the momentum operator do not communte，the re-ordering of the coordinate and the momentum operator functions is a fundamental problem in quantum mechanics. Using the completeness of coordinate and momentum representation and the integration within ordered product of operators，the re-ordering formulas of the coordinate operator and momentum operator function can be easily derived. In particular，a bivariate Hermite polynomial can be used to express the re-ordering of the power of coordinate and momentum exponential operator neatly. Furthermore，the structure of the coordinate-momentum intermediary representation can be derived by the integration within ordered product of operators.
Semi-general solution of second-order ordinary differential equation and its application in mathematical physics
QU Kui，NI Zhi-xiang
College Physics. 2018, 37(10): 7-9. doi:
10.16854 /j.cnki.1000-0712.180123
Abstract
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1881
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434
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Taking the second-order linear ordinary differential equation as an example，the concept of semigeneral solution of differential equation is introduced，and some typical applications of semi-general solution in solving mathematical physics problems are given.
Theoretical discussion of the precision of geostationary orbit
HAO Ji-guang1，HU Ya-xin2，HUANG Yi-bin2
College Physics. 2018, 37(10): 10-11. doi:
10.16854 /j.cnki.1000-0712.170325
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1277
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288
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The high precision of geostationary orbit is discussed theoretically，and the general deviations from the geostationary orbit in the equator plane are obtained. Two examples are given.
Electric field in the cavity of a charged thick ellipsoidal shell
YU Feng-jun
College Physics. 2018, 37(10): 12-14. doi:
10.16854 /j.cnki.1000-0712.180127
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1408
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688
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The electric field inside the cavity of a uniformly charged thick ellipsoidal shell is calculated. This shell is composed of non-conductor. Its inner and outer surfaces are two coaxial ellipsoidal surfaces with the same eccentricity ratios. The method is used to divide this thick ellipsoidal shell to infinite thin ones. Firstly，the charge distribution of the thin ellipsoidal shell is calculated. In comparsion with the charge distribution of the charged conducting ellipsoidal surface，the electric field in the thin ellipsoidal shell is found. Finally，with the help of the superposition principle of electric field，the electric field in the cavity of thick ellipsoidal shell equals zero is found.
A study of two-dimensional damping motion of charged particles in uniform magnetic field
LANG Jun，DONG Hong-qiong
College Physics. 2018, 37(10): 15-20. doi:
10.16854 /j.cnki.1000-0712.180059
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1354
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519
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In this paper，we analyze the law of motion of charged particles by the synergy of Lorentz force and resistance，including particles movement distance，rate changing over time，kinematic equation，trajectory，final displacement and maximum displacement.
Perturbation filtration system with weak resonance signal
LI Huan-huan，LUO Ze，XIAO Hong-yang，XU Yu-zhou，PENG Chuan-qian
College Physics. 2018, 37(10): 21-24. doi:
10.16854 /j.cnki.1000-0712.180051
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1198
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233
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A perturbation filtration system for physical quantity measurement of weak resonance signal is introduced. With this system，the perturbation of a strong damped vibrating system is decreased and the resonance state of the vibrating system can be determind. The relative physical quantity can be measured accurately.
Measurement of Young’s modulus of aluminum plate by digital holographic comparison
YAN Qi-qi，CHEN Yan，HU Xiang，ZHAO Xin-zhu
College Physics. 2018, 37(10): 25-29. doi:
10.16854 /j.cnki.1000-0712.180030
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1412
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300
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The measurement of tiny displacement is one of the applications of holographic interferometry，and the digital holography，which is a combination of the traditional optical holography and the digital technology，is a relatively new method of getting optical information. In this paper，the technology of digital holography is applied to the existing physical experiment teaching of optical holographic，and the tiny displacement variables of aluminum plate which is derived from the effect of external force，is measured by digital holography comparison method. According to the experimental data measured，Young's modulus of aluminum plate is obtained by the calculation formula，then which is compared with the measurement result of traditional optical holography method under the same experimental environment and the given standard values of aluminum plate. The experimental results show that the digital holography comparison method does not only omit the processing procedure in optical holography such as optical exposure and chemical wet treatment etc.，shortens the experimental operation time，but also reduces the influence of external environment factors，improves the accuracy of the measurement result. The relative error between the measurement result acquired by this method and the given standard value is 3.9%.
Theoretical and experimental fusion teaching research of Hall effect and magnetoresistance effect
YU Jing-xia，HUO Zhong-sheng，GUO Yuan-jun，YAO Lie-ming，CHEN Qun-yu，
College Physics. 2018, 37(10): 30-35. doi:
10.16854 /j.cnki.1000-0712.170686
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2327
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Both college physics and college physics experiment are two deeply fused courses. In this article， the fusion teaching method about Hall effect and magnetoresistance effect，which are two hot spots of modern physics research and application in the two courses，is investigated. Three aspects of teaching content are proposed in theoretical fusion，experimental fusion and mutual fusion between theory and experiment.
A simplified method for lifetime measurement of cosmic ray muons
TIAN Yi，HU Lu-guo，SUN Bao-hua
College Physics. 2018, 37(10): 36-37. doi:
10.16854 /j.cnki.1000-0712.180148
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2132
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881
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The muon is the main part of cosmic rays which can be detected on the Earth’s surface and an elementary particle of standard model. The muon decays to an electron and neutrinos. The lifetime measurement of muon can help students to know the decay properties of muon and also the time dilation effect of special relativity. In this paper，a NaI( Tl) detector is used to detect the signals of stopped muon and its decay electron. A simplified experimental method is introduced to measure the mean lifetime of muon in the laboratory
The integrated development of curriculum and teaching materials for the construction of first class undergraduate teaching
WANG Lei, NI Mu-cui, ZHANG Han-zhuang
College Physics. 2018, 37(10): 38-40. doi:
10.16854 /j.cnki.1000-0712.180292
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1487
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This paper analyzes the relationship between curriculum and teaching materials，puts forward the author's thinking about the connotation，types and ways of the integration of curriculum and teaching materials. The practice，experience，and teaching achievements of the author and his team to promote the integrated development of curriculum and teaching materials in the teaching of physics courses in jilin university are introduced.
Quantitative study on the vibration of the siren membrane
CHEN Sheng-nan, BAI He
College Physics. 2018, 37(10): 41-46. doi:
10.16854 /j.cnki.1000-0712.180105
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1772
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758
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Based on the theoretical study of free vibration of plane film，combined with the Eighth National College Physics academic competition，the phenomenon of sound vibration of the whistle is studied. According to the free vibration equation of the circular film，the different modes of the circular film vibration are analyzed by using the Bessel function. We make the 3D printing technology to make different specifications of the whistle. The circular tube changes the experimental condition，we use a high-speed camera to record the vibration process of the circular film，and use the Audacity software to analyze the fundamental frequency of the circular film vibration. The quantitative study of the vibration of the circular film is realized. The results show that the size of the tension of the circular film in the vibration is the choice of the vibration mode in the linear interval of the elastic deformation of the circular film. The main factor is that in the same vibration mode，changing the length and inner diameter of the whistle tube has no effect on the vibration form.
Ramsauer-Townsend effect and Child-Langmuir law experiments
ZHAO Yuan-sheng， JIA Xiao-han，YAO Hong-ying
College Physics. 2018, 37(10): 47-53. doi:
10.16854 /j.cnki.1000-0712.170632
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2072
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507
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Using a Hartree-polarization potential，the curve of the Ramsauer-Townsend effect obtained by a thyratron is analyzed. We also quantitatively investigate the phenomenon which occurs in the experiment of the Child-Langmuir law that the slope between ln I and ln Va ( where Va is the accelerating voltage) is less than 3 /2，by considering that the electrons have initial velocity.
Simulation and experimental study of Fresnel acoustic lens based on half-wave zone method
CHEN Bin-xin1，ZHU Hao-yu2，TU Hong-ye1，LI Jin-hua1，ZHANG Ye1，JIN Guang-yong1
College Physics. 2018, 37(10): 54-59. doi:
10.16854 /j.cnki.1000-0712.170697
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1449
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639
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In order to investigate the focusing ability of half wave acoustic band lens，the geometric formula of the two-dimensional ( 2D) half wave acoustic lens is obtained by using the Fresnel diffraction principle. A 2D axisymmetric physical model of the half- wave acoustic lens is established，and the finite element method is used to simulate the model-Holmholtz equation. Based on the physical model，the influence of the frequency，the number of half band and the transmission coefficient of the acoustic lens on the focusing ability are investigated. The results show that the increase of the number of half-band increases the sound pressure level at the focal point and change the position of the focal point. The lower the frequency is，the smaller the focal length is. The larger the transmission coefficient is，the smaller the sound pressure level at the focal point is. Finally，the effectiveness of the physical model is verified by making a simple acoustic lens.
Demonstration of several quantum phenomena by loaded string
HU Jing-yi，YANG Ai-ni，WANG Wen-zhu，BAI Zai-qiao，GONG Wen-ping
College Physics. 2018, 37(10): 60-65. doi:
10.16854 /j.cnki.1000-0712.180168
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1378
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459
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Loaded string is constructed by bonding some masses on a homogeneous string. When the elastic wave travels on the string meet one of the masses，it will partly penetrate the mass and partly reflect back，this is similar to the action of a potential barrier or well on quantum probability wave. Based on this similarity，we demonstrate in this paper the avoided crossing of energy levels，energy band in periodic structure and localization of eigenstate in random structure by the dynamics of a loaded string. We hope this experiment that can help students to understand those intriguing quantum phenomena.
Just Accepted
