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    15 August 2024 Volume 43 Issue 7
      
    An approach to introduce the expression of the momentum  operator in the coordinate representation
    SUN Ya-ting, WANG Feng
    College Physics. 2024, 43(7):  1.  doi:10.16854/j.cnki.1000-0712.230387
    Abstract ( 179 )   PDF (535KB) ( 165 )  
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    In quantum mechanics, operators and state vectors have different mathematical representations in different representations, allowing for the choice of a suitable representation to study specific problems. In most university physics textbooks, the introduction of the expression of the momentum operator in the coordinate representation is based on the basic assumption that the wave function of a free particle in the coordinate representation is a plane wave, which leads to a less rigorous mathematical derivation and causes confusion among students. In this paper, we propose a new approach to derive the mathematical expression of the momentum operator in the coordinate representation, combining the mathematical formula of Taylors translation operator and the fundamental commutation relation in quantum mechanics. This introduction method is more mathematically rigorous and more inspiring in teaching.

    Solving bound states in one-dimensional PT symmetric delta potential using Fourier transform
    JIA Chun-yu, LIANG Zhao-xin
    College Physics. 2024, 43(7):  3.  doi:10.16854/j.cnki.1000-0712.230370
    Abstract ( 105 )   PDF (586KB) ( 101 )  
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    Systems with PT symmetry are a hot topic in quantum mechanics research. The bound state problem in one-dimensional PT-symmetric delta potential well is the most simplified model of PT system, and its exact solution is a teaching problem with scientific research value. In this work, the effect of PT symmetry on the bound state and the intrinsic energy of a system is studied by solving the stationary Schrdinger equation of one-dimensional PT-symmetric delta potential. Firstly, the stationary Schrdinger equation of one-dimensional PT-symmetric delta potential is solved and discussed by Fourier transform. Secondly, the contours of the bound states and the intrinsic energies of the system are determined by numerical means. Finally, the relationship between PT symmetry potential strength and intrinsic energy is analyzed and discussed. In this paper, the traditional Hermitian delta potential well eigenvalue problem is extended to non-Hermitian delta potential well problem, which is a useful and timely extension of the necessary exercises in quantum mechanics teaching.
    Theoretical exploration of uncertainty in three-dimensional radial position and radial momentum using the circular orbit of hydrogen atoms
    SUN Hua-yang, CHEN Li-xiang
    College Physics. 2024, 43(7):  6.  doi:10.16854/j.cnki.1000-0712.230450
    Abstract ( 94 )   PDF (636KB) ( 64 )  
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    In a Cartesian coordinate system, linear position and linear momentum satisfy the uncertainty relationship, ΔxΔp≥2. Recent years also witnessed the research interest as to whether the radial position and radial momentum satisfies the similar uncertain relationship, in which one of the key points is how to construct a radial operator that satisfies the self-adjoint condition. Here, inspired by the two-dimensional hyperbolic momentum operator, we theoretically study the uncertainty relationship between the three-dimensional hyperbolic momentum operator and the radial position logarithm. Taking hydrogen atoms as an example, the products of the uncertainty of radial position logarithmic and that of three-dimensional hyperbolic momentum, i.e., Δln rΔPH, for different circular orbits are calculated. It is found that as the main quantum number increases, the wavefunctions of circular orbits are more approaching to the intelligent states.

    Investigating on two basic problems on vertical small vibration of thin circular or sectorial plate
    FANG Yi-zhong, SHEN Han, CUI Xin-tu, LIAO De-ju, FENG Rao-hui, WANG Gang
    College Physics. 2024, 43(7):  11.  doi:10.16854/j.cnki.1000-0712.230408
    Abstract ( 61 )   PDF (559KB) ( 86 )  
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     The vertical vibration of thin circular or sectorial plate under small flexivity theory is further investigated, and the natural boundary condition problem at the center of circle is discussed. The mistakes in several relative literature are analyzed and corrected. In the process of using variable-separated method to seek the solution of vibration on sectorial plate, the results are unrelative to the order of solving the angular and radical direction function, the classical views on boundary condition agree with the outcomes of variational method. It is concluded that the traditional theories of thin plate on solving the vertical small vibration problems are all proper up to present.

    A brief talk about the status and teaching skill of vector potential and dipole radiation in college physics teaching
    WANG Jun, ZHANG Zhi-ya
    College Physics. 2024, 43(7):  16.  doi:10.16854/j.cnki.10000712.230249
    Abstract ( 60 )   PDF (708KB) ( 89 )  
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    The introduction of the concept of vector potential in the teaching of general physics can help students deepen their understanding of electrostatic field and static magnetic field on the basis of comparative comparison. At the same time, with the help of simple vector operation rules, it can also show mathematical explanations for the dipole radiation as the basic composition of electromagnetic radiation. Such understanding about vector potential and dipole radiation will be helpful for the learning and articulation of subsequent courses.

    Study of dimensionality-dependent thermionic emission mechanism in semiconductor Schottky heterostructures
    ZENG Shu-ming, NI Jia-yi, WANG Wei, YANG Jin-peng
    College Physics. 2024, 43(7):  22.  doi:10.16854/j.cnki.1000-0712.230326
    Abstract ( 94 )   PDF (615KB) ( 69 )  
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    In this paper, classical thermionic emission model is employed to explore the formulas and their evolution for derivation of thermionic emission current in semiconductor Schottky junctions under three-dimensional, two-dimensional, and one-dimensional scenarios. These extended formulas can be widely applied to current research hotspot of interface barrier extraction and analysis in low-dimensional semiconductors, and should further contribute to enhancing students' understanding of semiconductor knowledge and the integrated application of related scientific research and analytical methods.

    Quantum geometric tensor in generic parameter space
    LI Xin, ZHANG Lin
    College Physics. 2024, 43(7):  25.  doi:10.16854/j.cnki.1000-0712.230364
    Abstract ( 146 )   PDF (661KB) ( 116 )  
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    The real and imaginary parts of quantum geometric tensor are of great significance and they can help us to understand the geometric and topological properties of quantum systems clearly. In this paper, from the case of gauge transformation acting on the real space and then extending it to an abstract parametric space, the tensors of quantum geometry with their relevant concepts are introduced in detail, which enable us a further understanding and a deep recognization of quantum geometry for quantum applications.

    Experimental study of metal surface damage measurement based on skin effect
    ZHOU Rong-hao, WANG Zi-zhen, LIU Jun, ZHAO Song-qin
    College Physics. 2024, 43(7):  31.  doi:10.16854/j.cnki.1000-0712.230381
    Abstract ( 74 )   PDF (771KB) ( 71 )  
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    Metal fatigue and damage mostly occur on the surface in early stages. When high-frequency alternating current excites the metal to be tested, the current mainly flows through metal surface due to skin effect. In this paper, the analysis of a model of cylindrical metal surface damage shows that these damages prevent the current from passing near the surface, and this result in a significant increase in highfrequency resistance. Phaselocked amplifiers are used to measure the voltage across copper and iron at different degrees of damage under different frequencies of AC excitation. The changes of resistance with frequency are calculated and compared. The results show that the resistance difference of samples with the same specification and different damage degrees is very small at low frequency and remarkable at high frequency. The experiment proves that skin effect can highlight the influence of metal surface damage on AC resistance of samples. The degree of surface damage of sample can be sensitively characterized by measuring the high-frequency skin resistance of metal. This nondestructive testing method is relatively sensitive. It can be used to detect the fatigue degree of metal samples as a whole, not as point by point. This method can save cost.

    Investigation of the normal distribution of random errors by labVIEW virtual instrument technique
    ZHAO Xiao-hong, WANG Shi-hong
    College Physics. 2024, 43(7):  37.  doi:10.16854/j.cnki.1000-0712.230264
    Abstract ( 83 )   PDF (859KB) ( 85 )  
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     In this paper, the virtual instrument technology LabVIEW as a software platform, combined with NI-USB6009 data acquisition card is used to measure DC voltage and both the amplitude and the frequency of sine wave of the signal generator. The statistical result of the measurement shows the normal distribution. For the periodic signal, increasing of sampling quantity per period can reduce the standard deviation of the frequency, and can cause improving the accuracy of frequency measurement. This experiment can be designed for students to study the normal distribution law of random error through practical measurement.

    An experimental system for directly measuring the quantized  energy of matters
    WANG Ying, WANG Zhi, ZHAO Yu-qiong, LUO Xiao-yu, TIAN Zhao-yang, SONG Jia-yi, LU Hao
    College Physics. 2024, 43(7):  41.  doi:10.16854/j.cnki.1000-0712.230275
    Abstract ( 65 )   PDF (704KB) ( 76 )  
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    Based on grating diffraction and machine vision, an experimental system for intuitively measuring quantized energy of matter is designed. It includes a blind box light source that excites luminescence of tested substances, a grating diffraction component,and a spectrum reading system. This novel system can measure energy levels or bands of different substances in different ways and achieve real-time data processing. Blind box light source utilizes the basic principles of photoluminescence or electroluminescence to stimulate electrons in tested substance to transition from valence band to conduction band, and emit the fingerprint signal of light of a specific wavelength. The diffraction spectrum is obtained by classical grating diffraction method. Besides, diffraction spectrum is collected in real time by digital camera, and the center position of diffraction spot is automatically obtained through image processing algorithms to reduce the spectrum reading error. This experimental system intuitively and conveniently demonstrates the quantized energy of matters.



    Measuring the diameter of superfine wire by laser diffraction
    LIU Jun, ZHOU Rong-hao, ZHAO Song-qing
    College Physics. 2024, 43(7):  46.  doi:10.16854/j.cnki.1000-0712.230376
    Abstract ( 169 )   PDF (679KB) ( 129 )  
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    Based on the principle of laser diffraction, a method of measuring the wire diameter which is less than 12μm is introduced. Using the least square method fitting the diffraction intensity of the central bright stripe, the wire diameter can be obtained in high-precision. Carbon fiber and Xinjiang long-staple cotton are used as samples, and three lasers with different wavelength are used to carry out the experiment. It is realized that accurate experimental results can also be obtained by using low precision teaching light intensity detectors and smart phone light sensors.

    Research on light interference and diffraction phenomena by using linear  array detectors
    PANG Guo-wang1, LI Ping1, LI Xiao-Yun1, SUI Cheng-hua2, WANG Fei2, YANG Hao2, FANG Xin-ting2
    College Physics. 2024, 43(7):  50.  doi:10.16854/j.cnki.1000-0712.230415
    Abstract ( 63 )   PDF (642KB) ( 62 )  
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    The interference and diffraction phenomena of light are important contents of wave optics. Studying this phenomenon not only deepens the understanding of the wave nature of light, but also helps to further learn modern optical experimental techniques, such as spectral analysis, crystal structure analysis, holography, optical information processing, etc. In this article, a CCD linear array detector (Toshiba TCD1304) I used as one-dimensional light intensity distribution detector and corresponding circuits and software is developed. The relative distribution of light intensity is measured for various single and double slits. The results clearly show the characteristics of interference and diffraction. The relationship curve between position and light intensity is given in real-time. The apparatus has the superior characteristics of simple structure, high position resolution of 0.01 mm, sensitivity range of light intensity that can simultaneously measure single slit diffraction fringes of more than 8 levels, relative error between experimental results and theoretical values less than 5%, and dynamic data refresh rate of 30 ms/frame.

    Error analysis of electro-optic coefficient of lithium niobate crystal
    OU Jian-wen, CHEN Hui-qing, LIU Yi-min, ZHU Chang-yong, XIONG Hui, HOU Qi-zhe, LAI Kan, LI Xin-xia
    College Physics. 2024, 43(7):  54.  doi:10.16854/j.cnki.1000-0712.230343
    Abstract ( 106 )   PDF (569KB) ( 62 )  
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    The electro-optical coefficient is an important parameter of lithium niobate crystal, which is closely related to the design and application of electro-optical devices. However, the synthesis conditions of lithium niobate crystals are different and this results in different electro-optical coefficients of each crystal, which brings difficulties to the error analysis of electro-optical coefficients. From the perspective of numerical analysis, Python, the open source package is used to fit the measured data. The specific value of fitting parameters and their uncertainties are obtained, and then the electro-optical coefficient of crystal is derived from the error transfer theory. Numerical analysis shows that the half-wave voltage method has high accuracy in measuring electro-optic coefficient, and its relative error is less than 2%. The fitting code of the widely used program Python is also given in this paper, and relevant researchers are welcome to use for reference.

    Exploring and practicing of ideological and political education in electromagnetism
    TANG Jun, ZHANG Rong, CHEN Ling-xiu
    College Physics. 2024, 43(7):  59.  doi:10.16854/j.cnki.1000-0712.230271
    Abstract ( 95 )   PDF (644KB) ( 89 )  
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    As one of the most traditional branches of physics, complete theoretical system of electromagnetics has been constructed for a long history. This makes electromagnetics naturally contain rich curriculum ideological content, including scientific ideas, exploratory spirit  and national confidence. In this paper the educational connotation of the course is condensed and the ideological and political elements are systematically collected and organized based on the educational connotation. The ideological and political elements of the course are organically integrated into the teaching design according to the teaching content. Some ideological and political elements of electromagnetism are shown in this paper. Taking two teaching segments as examples, part of the teaching design considering integrating ideological and political education is shown. 


    Simulation of object motion under viscous resistance based on VPython
    QU Hao-ran1, LIU Yv-ying2, ZHAO Zhi-chao2, ZHAO Yun2, HE Zhi-wei3
    College Physics. 2024, 43(7):  63.  doi:10.16854/j.cnki.1000-0712.230272
    Abstract ( 76 )   PDF (679KB) ( 51 )  
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    During college physics teaching, viscous resistance and terminal speed are very important concepts in applying the Newton’s laws. In this paper, we compare and analyze the knowledge points of viscous resistance and terminal velocity, and simulate the motion of objects which experienced viscous resistance by VPython software, such as dandelion seeds, basketball,and the Shenzhou spaceship. Most interestingly, based on the constant mass of object, we also study and simulate the falling motion of raindrop of varying mass with the effect of viscous resistance. The results indicate that the raindrop will approach its terminal speed which is relative to the radius of raindrop. The simulation deepens the understanding of textbook knowledge.


    Electric field distribution of regular hexagon line charge 
    ZHANG Nan, WANG Ping, XIE Ting-yue, TIAN Cui-feng
    College Physics. 2024, 43(7):  69.  doi:10.16854/j.cnki.1000-0712.230261
    Abstract ( 102 )   PDF (793KB) ( 132 )  
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    As an important physical model, the study of electric field distribution of line charge has great physical significance. In this paper, by using the symmetry of regular hexagon, formula of electric field intensity about charged finite length-straight line and superposition principle are used to solve the distribution of electric field intensity and potential on central axis and asymmetric axis of regular hexagon line charge. At the same time, in order to understand the distribution more directly and simply, MATLAB simulation software is used to draw the field distribution of the regular hexagon line charge, and the law of the electric field strength is obtained by analysis. On both the symmetric and asymmetric axes, the distribution of electric field direction is odd symmetric, and the intensity of electric field is mainly localized near the regular hexagonal line charge. On the symmetric axis, the strength is higher, but the range of intensity is smaller than that on the asymmetric axis. The distribution of electric potential is symmetric on both axes, with the highest potential near the line charge on asymmetric axis.

    A liquid conductivity measurement methodby correcting spontaneous electromotive force
    CHEN Yi-ting1, NI Jun-hao1, LU Hao-nan1, LI Yu-chen1, DONG Shi-lian2
    College Physics. 2024, 43(7):  74.  doi:10.16854/j.cnki.1000-0712.230273
    Abstract ( 89 )   PDF (741KB) ( 50 )  
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    A novel liquid conductivity measurement method based on the principle of bridge balance is proposed. The accuracy of conductivity measurement is affected by inherent capacitance and spontaneous electromotive force of liquid, which are encountered in conventional testing processes. To mitigate the interference caused by capacitance, high-frequency alternating current is employed instead of direct current. Additionally, an oscilloscope is used as a replacement for a galvanometer optimizes the criteria for bridge balance determination. Specifically, the oscilloscope indicates a non-zero linear signal as the reference for bridge balance. Based on this method, it is observed that the concentration of sodium sulfate solution exhibits a linear relationship with its conductivity. The relative uncertainty can be reduced to as low as 1.8%. This finding can be successfully applied in blind predictions of unknown solution concentrations and simulated rainfall amounts.

    Imaging deviation analysis of object points on axis through  biconvex symmetrical spherical lens
    YU Chen-xi, FENG Li-feng, SUN Wen-jun
    College Physics. 2024, 43(7):  81.  doi:10.16854/j.cnki.1000-0712.230303
    Abstract ( 73 )   PDF (613KB) ( 76 )  
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    In order to determine the difference between the ideal imaging and the real imaging produced by the object point on the axis passing through the biconvex symmetric spherical lens, and to verify whether the imaging device can meet the requirements of practical imaging application, the boundary equation of the imaging region of the object point on the axis passing through the biconvex symmetric spherical lens is derived by using the analytical geometry method, and the influence of the Angle of incident ray and the lens parameters on the imaging region is calculated and analyzed. The results show that when the object point position on the axis and the radius of curvature of the lens are determined, for example, the object distance is 30.0 cm, the radius of curvature is 15.0 cm and the half thickness of the lens L≤0.300 cm, the deviation on the axis representing the degree of deviation from the ideal imaging point on the boundary axis of the imaging region is less than or equal to 2.02%; when the object point position on the axis and the lens parameter are determined, for example, the object distance is 30.0 cm, the lens half-aperture h=3.00 cm and the angle of incident ray α≤4.85 °, the off-axis deviation representing the off-axis degree of imaging points at the boundary of the imaging region is less than or equal to 10%. This method can also analyze other aberrations. The theoretical derivation and calculation results provide theoretical support and technical reference for the subsequent research.