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    13 March 2026 Volume 44 Issue 12
      
    Cultivation of top physics talents in the era of artificial intelligence
    CAO Qinghong1, LIU Jia1, WU Taoli1, WANG Xiaoping2, LI Bin3, SANG Haibo4
    College Physics. 2025, 44(12):  1.  doi:10.16854/j.cnki.1000-0712.250378
    Abstract ( 151 )   PDF (745KB) ( 132 )  
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    This paper systematically explores the role and pathways of artificial intelligence (AI) in cultivating top-tier talent in the field of physics. It analyzes AIs educational potential in enhancing teaching efficiency,optimizing learning experiences,and enabling personalized support. Using examples such as the problem-based collaborative teaching model (TSAI) and AI-empowered undergraduate research training,the study examines practical implementations of AI in physics education. AI is positioned not merely as a technological tool but as a driving force for transforming educational philosophy and learning approaches. By leveraging the complementary strengths of humans and AI through human-AI collaboration,the approach aims to foster students abilities in questioning,decision-making,and innovation,thereby reinforcing the educational value of physics. Finally,the paper offers practical recommendations for integrating AI into physics education,providing theoretical and practical insights for talent cultivation in higher education.

    Measurement of electron spin energy levels based on NV center  ensembles in diamond
    YU Tongpo, LIN Hui, FAN Jingwei, ZHANG Ting, LI Zhongjun, CHEN Bing
    College Physics. 2025, 44(12):  9.  doi:10.16854/j.cnki.1000-0712.250185
    Abstract ( 131 )   PDF (1094KB) ( 42 )  
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     A quantum energy level measurement experimental setup based on an ensemble of NV centers is designed and implemented. By combining optically detected magnetic resonance (ODMR) technology, this setup achieves high-sensitivity measurements of electron spin energy levels at low cost. Using nanodiamond clusters to enhance fluorescence signals and integrating confocal microscopy systems with microwave frequency sweeping techniques, the Zeeman effect and temperature response of electron spin energy levels are observed at room temperature. This experimental scheme is suitable for college physics education, helping students understand the principles of quantum energy level measurements and solid-state quantum sensing technologies. 

    Cylindrical coordinate representation of the Biot-Savart #br# law and its applications
    LI Ziliang1, LU Ding2, WANG Weiyi1
    College Physics. 2025, 44(12):  16.  doi:10.16854/j.cnki.1000-0712.250286
    Abstract ( 113 )   PDF (554KB) ( 80 )  
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    The cylindrical coordinate formulation of the Biot-Savart law is derived by coordinate transformation between Cartesian and cylindrical systems. The derived formulation is applied to calculate the magnetic field distributions generated by infinitely long current-carrying solenoids and cylindrical conductors. The results demonstrate that the cylindrical coordinate representation of the Biot-Savart law significantly simplifies magnetic field calculations for current-carrying conductors with axial symmetry. Furthermore, the magnetic field distribution along the central axis of a current-carrying elliptic coil is also calculated. It is specifically noted that the coordinate scaling method proposed in some literature for calculating the magnetic field at arbitrary spatial points around such coils is unfeasible.


    Study on the two-dimensional Bragg scattering of wave packets
    WANGPu, DENGZhijiao, LINHuizu, CHENPingxing
    College Physics. 2025, 44(12):  20.  doi:10.16854/j.cnki.1000-0712.250012
    Abstract ( 74 )   PDF (790KB) ( 34 )  
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    The electron crystal diffraction experiment, which validated the de Broglie hypothesis of matter waves, is a significant event in the history of the establishment of quantum mechanics. This paper explores the phenomenon of Bragg scattering of massive particles, such as electrons, by numerically simulating the scattering process of wave packets in a two-dimensional periodic arrangement of delta potentials, supplemented by analytical calculations. The study demonstrates the evolution characteristics of the scattering process and analyzes the influence of relevant parameters on the scattering pattern, providing an intuitive physical picture for the teaching of high-dimensional scattering in quantum mechanics.


    Boundary Condition Application Methods for Uniform Magnetic Fields Based on Vector Magnetic Potential

    TANG Liezheng1, ZHANG Yuhao1, ZHOU Guohua1, BIAN Qiang1, GUO Yong2, ZHOU Yi3
    College Physics. 2025, 44(12):  25.  doi:10.16854/j.cnki.1000-0712.250076
    Abstract ( 66 )   PDF (1096KB) ( 25 )  
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    Magnetic field calculations with a uniform external field as the excitation typically formulate boundary value problems using scalar magnetic potentials. However, for eddy current magnetic fields and similar problems, the vector magnetic potential must be employed as the governing potential function. Currently, there are no published literature reports on the method for setting boundary conditions for uniform magnetic fields using the vector magnetic potential. To address this, this paper proposes two boundary condition application methods based on vector magnetic potential. The analytical solutions for the magnetic field are derived using the separation of variables method, and then finite element magnetic field simulations are conducted. Both analytical calculations and numerical simulations demonstrate that the proposed boundary conditions generate uniformly distributed magnetic flux density. The findings provide references for eddy current magnetic field simulations under uniform timevarying magnetic field excitations.


    Case analysis of “simultaneous relativity”
    JIN Fengtao, ZHANG Sen, GAO Cheng, WANG Xiaowei
    College Physics. 2025, 44(12):  29. 
    Abstract ( 61 )   PDF (655KB) ( 47 )  
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    In the study of special relativity, “simultaneous relativity” is a difficult point, and beginners are easily confused when transforming time and space between different reference frames. Especially deeply rooted daily experiences can bring a lot of confusion to the understanding of “simultaneously”. This paper designs two spacecraft flying towards each other and an observer on the ground. By comparing the clock timings of the three spacecraft, the common difficulty in understanding “relativity of simultaneity” in learning is demonstrated. In the analysis of the case, not only detailed calculations were carried out in different reference frames through Lorentz transformation, but also the effect of the principle of the constancy of the speed of light was intuitively demonstrated through the flashing experiment of the clock.


    Elegant application of residue theorem in calculating fidelity susceptibility #br# of one-dimensional XY model
    LUOQiang
    College Physics. 2025, 44(12):  35.  doi:10.16854/j.cnki.1000-0712.250205
    Abstract ( 47 )   PDF (845KB) ( 36 )  
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    The fidelity and its derivative, the fidelity susceptibility (FS), have emerged as pivotal concepts in quantum information theory and have garnered significant attention as robust probes for detecting quantum phase transitions. However, the derivation of analytical solutions for the FS remains a challenge, primarily due to the paucity of quantum integrable models. To address this issue, this paper employs the one-dimensional XY model as a paradigmatic example. Initially, a series of parameterized integrals are meticulously constructed, and their analytical expressions are adeptly derived through the application of the residue theorem. Subsequently, the intricate relationship between the FS and these parameterized integrals is elucidated across different phase transition processes, culminating in the derivation of a closed-form expression for the FS. This study underscores the crucial role of the FS in identifying quantum phase transitions and accentuates the remarkable efficacy and superiority of the residue theorem in tackling complex physical problems.


    Explanation of the coherence of light and the directional properties of lasers
    CHEN Peifeng, LV Xuan
    College Physics. 2025, 44(12):  40.  doi:10.16854/j.cnki.1000-0712.250204
    Abstract ( 76 )   PDF (448KB) ( 25 )  
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    This paper addresses students′ common difficulties in understanding the connection between the high directionality of lasers and their spatial coherence. It systematically analyzes the fundamental differences between conventional incoherent light sources and laser sources in terms of coherence and directional properties. By comparing theories of spatial coherence in physical optics and laser principles, the distinctions and intrinsic relationships between these concepts are clarified, providing theoretical support for students to gain a deeper understanding of the "four key characteristics" of lasers.

    A quantitative study on the interaction between charged particles in parallel
    HUANG Shaoshu1, 2, FENG Junjie2
    College Physics. 2025, 44(12):  44.  doi:10.16854/j.cnki.1000-0712.250166
    Abstract ( 103 )   PDF (457KB) ( 54 )  
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     Charged particles are assumed to be a standard geometric model, an expression for the migration current, displacement current, and magnetic induction intensity generated by the motion of charged particles is inferred based on the microscopic definition of current intensity, the law of total current, and the Biot Savart law. Further calculate the electric and magnetic field forces between two charged particles running parallel in vacuum, provide the velocity constraint relationship and velocity magnitude criterion for the electric and magnetic field forces, and compare their consistency with the relevant results obtained by considering relativistic effects. It is pointed out that only when the speed of charged particles is close to the speed of light, can magnetic field forces and electric field forces be comparable.


    Derivations of the singlet and triplet of two coupled electrons
    HUANGYong-yi
    College Physics. 2025, 44(12):  50.  doi:10.16854/j.cnki.1000-0712.250082
    Abstract ( 54 )   PDF (400KB) ( 22 )  
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    Using raising and lowering operators, we directly and naturally derive the singlet and triplet of two coupled electrons based on the uncoupled basis.

    The solution of the Poisson equation on a rectangular region #br# based on compact differences
    PEI Xiao-qi1, WANG Jia-hua2, TAN Jia3, YU Li-min1
    College Physics. 2025, 44(12):  52.  doi:10.16854/j.cnki.1000-0712. 240346
    Abstract ( 54 )   PDF (768KB) ( 23 )  
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    The Poisson equation is an important type of elliptic partial differential equation in the fields of mathematics and physics. It is one of the fundamental equations in electromagnetism and electrodynamics, with significant applications in plasma physics. Numerically solving the Poisson equation efficiently has been widely studied. The finite difference method is a common approach for numerically discretizing and solving such elliptic differential equations. The compact finite difference method, by introducing compact operators, can improve the computational accuracy of the finite difference method and reduce computational cost. In this work, we apply the compact finite difference method to numerically solve both the source-free Poisson equation and the linear Poisson equation with a source term within a rectangular domain. We also iteratively solve the source-free nonlinear Poisson equation. The analytical solutions and numerical solutions are visualized using Matlab. Meanwhile, the accuracy and reliability of the solver are verified by comparing the analytical solutions with the numerical solutions. This work is of great significance for solving various types of Poisson equations in physics and indicates that visualization plays an important role in the learning of mathematical physics methods.


    The packing fraction of icosahedral clusters
    LIU Zhi-guo, ZHAO Jing-geng, ZHANG Yao-hui, WANG Xian-jie, HUANG Xi-qiang, LIU Wei-long, L Zhe, SUI Yu
    College Physics. 2025, 44(12):  59.  doi:10.16854/j.cnki.1000-0712.250079
    Abstract ( 60 )   PDF (504KB) ( 24 )  
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    The existence of “magic number” is the fundamental characteristic of clusters. For clusters bound by van der Waals force, they can be described by the icosahedral model, which can well reproduce the magic numbers. Although the coordination number of the central atom of icosahedral clusters is 12, it is not close-packed. To support the cluster, the “atomic spheres” are tangent along the vertex direction. Currently, the detailed calculation about the packing fraction of a regular icosahedron cluster can be hardly found. In this paper, we calculate it by spherical geometry. It decreases as the number of atomic layer increases. When infinite layers are concerned, the packing fraction is 68.82%, which is between the body-centered cubic and face-centered cubic (hexagonal close-packed) structures. The result can be referenced by colleagues engaged in teaching and investigation on clusters. 


    Application of the McMillan formula to hydrogen-based superconductors
    LI Bin
    College Physics. 2025, 44(12):  64.  doi:10.16854/j.cnki.1000-0712.250009
    Abstract ( 64 )   PDF (541KB) ( 20 )  
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    The McMillan formula is a crucial component of BCS superconductivity theory and a vital tool for predicting the superconducting transition temperature in conventional superconductors. This paper introduces the original McMillan formula and its Allen-Dynes modified version. Using hydrogen-based superconductor as example, we apply the McMillan equation to reveal the relationships between electron-phonon coupling strength, logarithmic phonon frequency, and superconducting transition temperature. Superconductivity and its electronic properties represent significant challenges and frontier topics in solid-state physics. Teaching solid-state physics should emphasize superconductivity-related issues and their role in modern physics.


    Potential energy of unchanged forces and its applications #br# in solving problem in theoretical mechanics
    CHEN Liqun1, 2
    College Physics. 2025, 44(12):  67.  doi:10.16854/j.cnki.1000-0712.250130
    Abstract ( 62 )   PDF (971KB) ( 39 )  
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    A unchanged force is demonstrated as a potential force with its potential energy to solve problems in theoretical mechanics. In equilibrium problems, the potential energy can be used to establish the equilibrium conditions for a potential system subjected to unchanged forces and the stability is determined via the stationary value of the potential energy. The potential energy generalizes the conservative Lagrangian equation to a potential system with unchanged forces. For Lagrangian functions independt of the time or the generalized coordinates, the generalized energy conservation and generalized momentum conservation are obtained.

    Self made onedimensional highprecision #br# flux gate magnetometer based on LabVIEW#br#
    ZUO Xueyang, HU Jiawei, BAI Luxing, WANG Aiji, BAI Zaiqiao
    College Physics. 2025, 44(12):  69.  doi:10.16854/j.cnki.1000-0712.250083
    Abstract ( 43 )   PDF (1302KB) ( 23 )  
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    This article presents the design and fabrication of two onedimensional highprecision flux gate magnetometers with ringshaped magnetic cores based on LabVIEW filter program, which are used for weak magnetic field measurement. Both magnetometers use a 1.5 kHz sine wave as the excitation signal. Differently, the No.1 magnetometer uses 1k107 thin tape as the magnetic core material, with a measured sensitivity of 2.913×10-4  V/μT, a minimum resolution of 56.0 nT, and a range of approximately 1300 μT; The No. 2 magnetometer uses 1j85 thin tape as the magnetic core material, with a sensitivity of 3.050×10-4 V/μT, a resolution of 99.5 nT, and a range of approximately 600 μT. The experiment verified the measurement ability of the magnetometer in four typical magnetic fields (geomagnetic field, Helmholtz coil, DC wire, and small magnet magnetic field), and the measured magnetic field distribution was consistent with theory.


    A new method for measuring the moment of #br# inertia of a Stirling heat engine System
    LI Lingyan1, LIN Hewei1, XIAO Yangming1, FENG Zhihao1, WANG Aini1, LI Zhuanghua1, YOU Chunlian1, WANG Zhaoming2
    College Physics. 2025, 44(12):  79.  doi:10.16854/j.cnki.1000-0712.250132
    Abstract ( 37 )   PDF (831KB) ( 14 )  
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    Based on the Stirling heat engine model, a new method for measuring the system moment of inertia is proposed. This method eliminates the need to disassemble experimental setups. By simply connecting a load generator to the running Stirling heat engine system, the moment of inertia can be indirectly determined through measurements of the load generators output power, along with angular acceleration and angular velocity during the deceleration phase after loading. Comparative experiments with the traditional moment of inertia measurement methods demonstrate that this approach exhibits high validity and accuracy. The proposed method provides new perspectives and research pathways for measuring the moment of inertia in structurally complex experimental systems or those difficult to disassemble. It provides new ideas and application value for measuring the moment of inertia of flywheel systems driven by different types of driving forces.

    Fast search algorithm for configuration parameters with  isochronous normal and inverted oscillations in Kater pendulum
    CHEN Liheng, YU Dan, GAO Yonggui, ZHOU Liang
    College Physics. 2025, 44(12):  83.  doi:10.16854/j.cnki.1000-0712.240555
    Abstract ( 26 )   PDF (760KB) ( 16 )  
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    A crucial step in measuring gravitational acceleration using a Kater pendulum is to equalize the periods of its normal and inverted oscillations. This paper takes the oscillating period difference of a Kater pendulum in its normal and inverted configurations as the objective function, and presents a monotonicity and sensitivity analysis of this function with respect to three configuration parameters: hanging point, large bob, and small bob positions. Based on this analysis, we propose an efficient algorithm for finding the configuration parameters with isochronous normal and inverted oscillations in Kater pendulum, significantly reducing the number of adjustments required and substantially improving experimental efficiency.



    Research on teaching in the course of advanced electromagnetic #br# fields assisted by artificial intelligence
    BAO Yang1, LIU Ziyan1, ZHOU Fei1, CHEN Xinru1, WAN Ting2
    College Physics. 2025, 44(12):  89.  doi:10.16854/j.cnki.1000-0712.250156
    Abstract ( 48 )   PDF (756KB) ( 34 )  
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     “Advanced Electromagnetic Fields” is a core and foundational course for students majored in the electromagnetic field and wireless technology, serving as the prerequired course for other courses such as microwave engineering and antenna theory. This course focuses on solving the integral and differential forms of Maxwell’s equations. Learning of each knowledge point is based on numerous formula derivations, with strong theoretical and abstract concepts. The integration of artificial intelligence (AI) methods into the “Advanced Electromagnetic Fields” course not only preserves the teaching of core knowledge concepts and ensures sustainable development of the curriculum, but also incorporates cutting-edge AI algorithms, effectively stimulating students’ learning motivation. This article will take the teaching of eddy current testing problems in the “Advanced Electromagnetic Fields” course as an example. It introduces artificial intelligence algorithms into the full-wave simulation calculations of complex and cumbersome detection responses, combining complex numerical computations with mainstream AI algorithms. This approach avoids abrupt and dull teaching methods, sparking students’ enthusiasm for learning. By integrating practical engineering cases of eddy current testing, it incorporates theory into practice, enhancing student engagement and stimulating their potential.


    The Researches of Magnetic Resonance Imaging by Lauterbur Paul
    YIN Xiaodong1, LIANG Jing2, LIU Zhancun1, FAN Shifu1
    College Physics. 2025, 44(12):  94.  doi:10.16854/j.cnki.1000-0712.240499
    Abstract ( 30 )   PDF (865KB) ( 22 )  
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    Lauterbur had long been committed to studying chemical structures using nuclear magnetic resonance. After observing that the relaxation time of malignant tissues in mice was significantly longer than that of their normal tissues, he pondered deeply on how to apply this characteristic to non-invasive examination of tumors in the human body in medicine. This led to the idea of using magnetic field gradients for spatial encoding in nuclear magnetic resonance. Through experiments with spectrometers, he laid the foundation for magnetic resonance imaging and continued to research magnetic resonance imaging technology. He regarded scientific research as his life. Seizing opportunities, emphasizing reverse thinking, not fearing criticism, and persisting in innovation — these qualities were important factors in his success.

    Light deflection in Euler-Heisenberg nonlinear electrodynamics
    DUAN Xingyu, MA Mengsen
    College Physics. 2025, 44(12):  104.  doi:10.16854/j.cnki.1000-0712.250189
    Abstract ( 47 )   PDF (651KB) ( 32 )  
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    Based on the Euler-Heisenberg nonlinear electrodynamics theory, we investigate the characteristics of photon propagation in the effective spacetime geometry under strong electromagnetic fields. By constructing a spherically symmetric curved spacetime model, we derive the effective metric equations governing photon motion and calculate the light deflection effect in a spherically symmetric gravitational field. Numerical results indicate that the nonlinear correction-induced deflection angle reaches an observable order of magnitude (arcsecond scale) only when the source charge attains an extremely high value of approximately 1010C.


    Recommendation for a frontier research monograph《Statistical Physics and Complex Transport of Biomolecular Motors》
    GAO Tianfu1, ZHENG Zhigang2, 3
    College Physics. 2025, 44(12):  108.  doi:10.16854/j.cnki.1000-0712.250236
    Abstract ( 39 )   PDF (883KB) ( 34 )  
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    Nonequilibrium transport is one of the most important and active frontiers in statistical physics of nonequilibrium and complex systems today. Biomolecular motors are typical nonequilibrium complex systems, and their nonequilibrium transport processes and statistical physics are the important contents in this field. Given the current lack of systematic monographs on molecular motors in China, we have authored the scholarly work《Statistical Physics and Complex Transport of Biomolecular Motors》. This monograph is rooted in the field of molecular motors, and the different types of ratchet models are established physically according to the diversity of motors. The biological complexity of directional transport generated by molecular motors are investigated by nonequilibrium transport theory, stochastic energetics and stochastic thermodynamics theory. This book is divided into 9 chapters, and shows the readers the basic problems and the new development in the field of molecular motors systematically. This monograph can be read by researchers of statistical physics and molecular motor, graduate students and senior undergraduates, and the monograph also has important reference value for researchers in cross fields related to biophysics.