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    20 March 2020 Volume 39 Issue 03
      
    Study of quantum transformation operator for singleoptical beam splitter
    REN Gang, DU Jian-ming, YU Hai-jun, ZHANG Wen-hai
    College Physics. 2020, 39(03):  1-3.  doi:10.16854 / j.cnki.1000-0712.190382
    Abstract ( 1467 )   PDF (204KB) ( 800 )  
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    The transformation matrix of the ideal single optical beam splitter is obtained. The unitary transformation operator of the single optical beam splitter is also given by using the coherent state representation and the inner integral technique of the order operator. The experimental preparation of entangled states shows that single optical beam splitter plays an important role in the study of quantum information sources.

    Correct usage of the dielectric constant of metal—demonstrated by the energy level shift of a ground two-level system around a metal nanosphere
    HUANG Yong-gang, WEN Sha-sha, YANG Hong, WANG Xiao-yun, DENG Ke, PENG Jin-zhang, ZHAO He-ping
    College Physics. 2020, 39(03):  4-8.  doi:10.16854 / j.cnki.1000-0712.190316
    Abstract ( 1150 )   PDF (706KB) ( 757 )  
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    The electromagnetic response of metal contains the contribution of the free charges and the bound charges,which are usually theoretically descripted by the Drude model and the Lorentz model in collage physics respectively. However,only in a certain frequency range that the prediction from both models agrees with the experimental values. In practical scientific research,one should make use of the experimental values of the dielectric constant instead of the results from the Drude model or the Lorentz model when the physical quantity is related to the response over a wide frequency range in principal. In this work,the energy level shift of a ground two-level system around a metal nanosphere is numerically demonstrated with the electric permittivity of metal from the Drude model and the experimental values. Significant difference is observed,which implies the importance of the correct usage of the electric permittivity of metal.

    Analogy of constant velocity field,electrostatic field and static magnetic field
    WU Bo-ying, ZHANG Shou-ping, FU Bo-qiao, PENG Xiao-xing, CHEN Jie
    College Physics. 2020, 39(03):  9-11.  doi:10.16854 / j.cnki.1000-0712. 190092
    Abstract ( 1482 )   PDF (492KB) ( 575 )  
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    By introducing the " physical analogy method" into the teaching of electromagnetic in university,a constant velocity field is compared with the electrostatic field and the static magnetic field in terms of the feature quantity,the distribution of the field and its description. This makes students have a clearer and more comprehensive understanding of the electromagnetic field,and have a deeper understanding and mastery of the theory of electromagnetism. A good teaching effect is achieved.

    Building of divergence concept from scratch
    LUO Ling-xiao
    College Physics. 2020, 39(03):  12-15.  doi:10.16854 / j.cnki.1000-0712.190301
    Abstract ( 1303 )   PDF (317KB) ( 582 )  
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    Without taking the Gaussian formula as a premise,the flux of the vector field passing through the infinitesimal closed surface is calculated from the beginning,so as to establish the divergence concept and derive the formula for calculating the divergence in the space rectangular coordinate system. Giving a beautiful area division formula,it can generally calculate the volume of the space area enclosed by the surface according to the shape and size of the closed surface. It is pointed out that people often fall into misunderstanding when they calculate the formula of the divergence by calculating the flux of the vector field through the surface of the infinitesimal hexahedron.

    The electric field in parallel plate capacitors with symmetrical vertical conductor ridges and its capacitance
    YIN Yong, WANG Fu-qian
    College Physics. 2020, 39(03):  16-19.  doi:10.16854 / j.cnki.1000-0712.180678
    Abstract ( 982 )   PDF (1297KB) ( 497 )  
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    The electric field of parallel plate capacitor with symmetrical vertical conductor ridge is studied by conformal mapping,and its potential distribution function and field intensity distribution function are given. The electric field lines and equipotential lines are plotted by MATLAB software,and its capacitance is calculated.

    Energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator in non-commutative phase space
    GOU Li-dan
    College Physics. 2020, 39(03):  20-23.  doi:10.16854 / j.cnki.1000-0712.190356
    Abstract ( 963 )   PDF (175KB) ( 366 )  
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    In non-commutative phase space,energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator is analyzed by using the invariant eigen-operator method. The explicit expressions for two kinds of three - mode harmonic oscillators: no coupling and coordinate - momentum coupling are obtained. Some expressions λ0,1 and λ1,1 have be connected with non-commutative parameters θ and φ,others λ0,2 and λ1,2 do not.It is discussed about theeffect of coupling parameters on energy spectrum of three-mode coordinate-momentum coupling harmonic oscillator.The results show that the coupling parameters κ and η have the similar effect on the λ1,1 .Furthermore,they do not have any effect on the λ1,1 when κ and η are equal.

    Solution of two simple Schrödinger equations by Fourier transform method
    LUO Guang, TAN Xin, LIU Ping
    College Physics. 2020, 39(03):  24-27.  doi:10.16854 / j.cnki.1000-0712.190308
    Abstract ( 2456 )   PDF (203KB) ( 1061 )  
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    The solution of Schrödinger  equation for free particle and one-dimensional infinite potential well is

    the basic content of quantum mechanics. In this paper, Fourier transform is used to solve these two

    simple Schrödinger equations. Through the in-depth discussion of the Fourier transform method of partial differential equation and the Fourier transform method of ordinary differential equation which separates from the partial differential equation by separated variable method,the results are consistent with those of relevant textbooks,and the differences and relations between the two methods are discussed.

    Discussion on the relationship between Novikov time and  Newton's absolute time of free fall
    YANG Zhi-wan
    College Physics. 2020, 39(03):  28-31.  doi:10.16854 / j.cnki.1000-0712.190386
    Abstract ( 1198 )   PDF (191KB) ( 676 )  
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    This paper firstly transforms the proper time (Novikov coordinate time)formula of the free-falling particle in the Schwarzschild black hole field from the form in the natural unit system to the form in the international system of units. Then,according to Newton's second law and the law of universal gravitation,the absolute time formula experienced by the free-falling particles is derived,which proves that the proper time of free-falling particle in general relativity is exactly equal to the absolute time given by Newtonian mechanics. Finally,a special case is calculated for the time that free-falling particle experience inside and outside the black hole.

    The optimum cycles in average“period”measurement of a simple pendulum:A solution based on uncertainty theory
    FENG Fei-long, WANGGong-zheng, WEI Fen-fen
    College Physics. 2020, 39(03):  32-35.  doi:10.16854 / j.cnki.1000-0712.190363
    Abstract ( 1813 )   PDF (607KB) ( 1165 )  
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    Due to the damping affected by air,when the average “period”is measured,it would decrease with the accumulated cycles. In the experiment in which zero damping is assumed,this accumulation wouldmake the systematic error increase and the random error decrease,simultaneously. Based on the motion equation and associated “period”formula of the simple pendulum in large-amplitude vibration and weak damping,the optimum accumulated times can be numerically calculated by searching the minimum uncertainty. It has been found that with different string lengths and amplitudes,usually more than 20 cycles should be measured once a time while in some cases when chronograph andphotogateis used,more than 1 cyclesare needed. If the average “period”could be measured for more times,the accumulated cycles in every time could optimally decreased effectively. With the optimal cycles,the uncertainty could get a minimum,about √2 times of the type A uncertainty.

    Design and research on focal length measurement method for thin lens
    FEI Xian-xiang, LI Cheng-peng, WANG Wen-hua, LI Yong-qiang
    College Physics. 2020, 39(03):  36-38.  doi:10.16854 / j.cnki.1000-0712.190149
    Abstract ( 2997 )   PDF (507KB) ( 1850 )  
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    This paper analyses the problems existing in the measurement of the foci of thin lens,and the method of parallax elimination is used to measure the focal length of thin lens. The first method uses self-collimation and eyes instead of eyepiece system,which can change the adjustment of the image clarity into the adjustment of the lateral object and image parallax,and can greatly reduce the error caused by the focal depth. The second method uses the conjugate method to measure the focal length by the symmetry of object and image,and at the same time skillfully uses the method of eliminating parallax. The measurement results show that the measurement results obtained by the method of parallax elimination are more accurate,reaching 0.4%.

    Analysis of the non-localized interference fringes  produced by Michelson interferometer
    GUO Dong-qin, CHEN Wen-bo, ZHANG Sheng-hai
    College Physics. 2020, 39(03):  39-43. 
    Abstract ( 4917 )   PDF (1080KB) ( 1865 )  
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    It is often found that there are non-circular quadratic fringes such as ellipse and hyperbola appeared

    in the experimental adjustment of Michelson interferometer. Aiming at this phenomena,this paper deduces the mathematical equation of the interference fringe based on the principle of non-local interference under the condition of point light source. On this basis,the shape of interference fringes under different conditions is analyzed. It is found that there are five kinds of line shapes of interference fringes can be acquired,they are circular,elliptic,parabolic,hyperbolic and straight. Based on the theoretical results,numerical simulation and experimental verification are carried out,and the numerical simulation results are in good agreement with the experimental results.

    Development of lasercollimating CCD digital spectrometer
    CHEN Guang-wei, LI Jing-wei, WEN Jing, XIA Xiang-fang, WANG Guo-you
    College Physics. 2020, 39(03):  44-46.  doi:10.16854 / j.cnki.10000712.190207
    Abstract ( 1005 )   PDF (1197KB) ( 418 )  
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    By using the semiconductor laser,the CCD display unit and a high precision solid axis angle sensor

    to improve the traditional spectrometer,the adjustment of spectrometer laser self-collimation can be achieved,which makes the coarse adjustment of spectrometer purposefully and reduces the blind adjustment. The liquid crystal display of telescope images alleviates the experimenters visual fatigue and reduces the parallax. The digital reading system makes not only readings become very simple and fast,but also the repeatability and reliability of data become better.

    Half-lifemeasurement of 89 Rb in neutron activation experiment
    FANG Kai-hong, ZHAO Jiang-tao, PENG Hai-bo, ZHANG Shuo, WANG Qiang
    College Physics. 2020, 39(03):  47-51.  doi:10.16854 / j.cnki.1000-0712.190370
    Abstract ( 1135 )   PDF (817KB) ( 588 )  
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    Neutron activation experiment is one of the important experiments in undergraduate experimental education. For further guiding students to dig experimental data,the half-life of fission nuclide ( 89 Rb)is measured simultaneously. In this paper,the fission reaction of 238 U induced by 14 MeV fast neutrons is carried out. The γ-ray energy spectrum of the fission products is determined by a low background HPGe ! γ spectrometer,and the half-life of 89 Rb is determined. In the data analysis,the two gamma rays of 89 Rb nuclide are independently used to obtain the half-life of 89 Rb of 15.30±0.09 min and 15.25±0.07 min. The measurement results are in good agreement with the data reported in the literature. This work improves the accuracy of the half-life of 89 Rb.

    How to derive the electromagnetic induction law and discover the  displacement current with a mechanical model by Maxwell
    SHEN Xian-yong
    College Physics. 2020, 39(03):  52-55.  doi:10.16854 / j.cnki.1000- 0712.190214
    Abstract ( 1782 )   PDF (1372KB) ( 977 )  
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    Maxwell equations is foundation of electromagnetics,and the equations is one of most beautiful equations in modern physics. The details of deriving the electromagnetic induction law and discovering the displacement current with a mechanical model are displayed.

    Otto Stern’s study of proton magnetic moments
    WANG Ya-ping, NING Chang-chun, ZHANG Hui-jie, HU Hai-bing
    College Physics. 2020, 39(03):  56-62.  doi:10.16854 /j.cnki.1000-0712.190254
    Abstract ( 1574 )   PDF (730KB) ( 1042 )  
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    Otto Stern won the Nobel Prize in Physics in 1943 for the development of molecular beam methods

    and the discovery of proton magnetic moments. In 1933,Stern and his collaborators measured proton magnetic moments.

    The measurement of proton magnetic moments expanded the way for human to explore the micro world and

    accelerated the process of people’s understanding of nuclear structure. The experiment of magnetic moment measurement

    has been carried out and the whole process of proton magnetic moment measurement by Stern et al. has

    been deeply excavated. The purpose is to clarify Stern’s pioneering contribution to proton magnetic moment measurement

    and the contribution of the experiment to the development of nuclear physics in the 1930s.

    The learning evaluation of college physics for deeper learning—taking freshmen to solve a mechanical problem as an example
    CHEN Yu-jie, HUANG Zhi-xin, WANG Qin
    College Physics. 2020, 39(03):  63-68.  doi:10.16854 / j.cnki.1000-0712.190273
    Abstract ( 1392 )   PDF (648KB) ( 458 )  
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    The quality of freshmen in college physics study is often evaluated with scores. With the development of deeper learning,another evaluation method which is based on the SOLO (Structure of the Observed Learning Outcome)taxonomy,divided students’thinking ability in the process of solving problems into five levels. The deeper learning theory divides these five levels into two levels:deep and shallow.Based on the above theory,this study classifies the thinking ability of freshmen when a mechanical problem is solved,evaluates the depth of their learning,and compares the above two evaluation methods and has found that the latter is more scientific,more observable and more suitable for teachers to evaluate the study of college physics for deeper learning.

    Comment on the history of thegeneral physics and its features
    CHENG Fu-ping, WANG Shuo, ZHANG Qi-wei
    College Physics. 2020, 39(03):  69-71.  doi:10.16854 / j.cnki.1000-0712. 180685
    Abstract ( 1172 )   PDF (120KB) ( 523 )  
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    The General Physics compiled by Cheng Shuozhu and Jiang Zhiyong is one of the earliest textbook of physics for science and engineering. It has been repeatedly revised during the last half century,and played great contribution in the important periods of teaching history. In this paper,we comment on its significant features from many respects including history and culture,fundamentals and frontiers,theory and practice,conclude that it is a good university physics textbook with a long history and constant improvement,and also exhibits its function of passing knowledge,fostering abilities and improving student’s qualities of science.

    The difference method forsolving the reaction-diffusion equation —Planetary cooling model as an example
    WU Jin-tai, LI Jin-da, JIANG Si-yi, LEI Lei, LI Xiang-hua
    College Physics. 2020, 39(03):  72-77. 
    Abstract ( 1385 )   PDF (1529KB) ( 847 )  
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    The reaction-diffusion equation is a kind of non-linear parabolic equation,which has been widely used in many physical models. An earth-like planetary cooling model is considered in this paper.Through reasonably assuming the heat conduction characteristics of each layer inside the planet,a set of reaction-diffusion equation is

      constructed.Also,different boundary conditions and initial conditions are deduced according to the actual physical

      situation.Then,based on the idea of finite difference method,the equations could be solved numerically by comput

      er programs.Finally,the variation of temperature distribution inside the planet with time is shown.