Table of Content

15 May 2026 Volume 45 Issue 2

  

Study on effective approaches to incorporating machine  learning into computational physics course——taking the application of SINDyPI algorithm in double  pendulum and Rssler systems as an example

WANG Xiaoyun1, 2, LI Wenyuan1, LIU Xiang2, 3

College Physics. 2026, 45(2):  1.  doi:10.16854/j.cnki.1000-0712. 250211

Abstract ( 48 )   PDF (932KB) ( 30 )  

Related Articles | Metrics

This paper begins by examining two simple classical nonlinear systems—the double pendulum system and the Rssler system. Through the use of the SINDyPI algorithm for identifying their dynamical equations, it demonstrates the efficiency and accuracy of machine learning methods in handling nonlinear systems and highlights the merits of this algorithm in datadriven approaches. Additionally, taking this as a basis, the study explores and discusses effective approaches to incorporating machine learning into the computational physics course. The findings provide valuable references for the practical implementation of teaching in computational physics.



Analytical solution of the Stoner Wohlfarth model

XUE Desheng, LIU Zhaochen, HU Yang

College Physics. 2026, 45(2):  7.  doi:10.16854 /j.cnki.1000-0712. 250304

Abstract ( 45 )   PDF (877KB) ( 25 )  

Related Articles | Metrics

The StonerWohlfarth model is a fundamental model in magnetism. However, the traditional solution methods can only provide analytical solutions for three specific angles. In this paper, by using the idea of inverse functions, a simple analytical solution for this model under general conditions is obtained. Using this analytical solution, the hysteresis loop describing static magnetism and the trajectory of magnetization intensity movement describing dynamic magnetism are obtained. The acquisition of this analytical solution provides a simple, intuitive and accurate scheme for quantitatively describing the stable direction of the uniform rotation of magnetization intensity and the precession image around that direction.






Two numerical methods for solving the energies and wave functions of  the threedimensional isotropic harmonic oscillator

XURenli, LIXiong, ZHURuxian, ZHAOZhizhen, DAILi

College Physics. 2026, 45(2):  11.  doi:10.16854/j.cnki.1000-0712.250305

Abstract ( 44 )   PDF (530KB) ( 25 )  

Related Articles | Metrics

This study numerically solves the Schrdinger equation for a threedimensional isotropic harmonic oscillator using Gaussian basis expansion and Fourier transform methods. Wave functions are constructed via Gaussian basis functions, with optimization of variational parameters to enhance the accuracy of energy level calculations. Additionally, the Fourier transform method is utilized to discretize the Schrdinger equation in momentum space, employing the fast Fourier transform algorithm to improve computational efficiency. Results are benchmarked against analytical solutions, and the applicability, accuracy, and computational efficiency of both methods are evaluated. This work serves as a reference for numerical computation teaching in quantum mechanics.



Equivalent form of RungeLenz vector

ZHENGXiaoJuan1, HUANGYibin2

College Physics. 2026, 45(2):  15.  doi:10.16854/j.cnki.1000-0712.250112

Abstract ( 34 )   PDF (530KB) ( 20 )  

Related Articles | Metrics

Through some simple derivations, a conserved vector in the inverse square force field is obtained, which is found to be equivalent to the Runge Lenz vector. We also discusse its relationship with the hodograph. 






On the universality of a concept of virtual displacement

ZHANGJiuzhu

College Physics. 2026, 45(2):  18.  doi:10.16854/j.cnki.1000-0712.250175

Abstract ( 35 )   PDF (558KB) ( 19 )  

Related Articles | Metrics

The article argues that defining virtual displacement as the difference of two possible displacements is more general. In this way, one can not only obtain the same commutative properties of derivative and variational operations and the commutative properties of integral and variational operations, but also obtain the Hamiltons principle. More importantly, one can study the virtual perturbations of more types of constrained systems and different types of virtual perturbations occurring in the same constrained system, so as to derive the equations satisfied by the generalized virtual displacements of the system. Meanwhile, for a general firstorder nonholonomic constrained system, whether it is subjected to a Jourdain virtual perturbation or a Gauss virtual perturbation, the Chetaev relation can be derived. The relation satisfied by the generalized virtual displacement of a firstorder linear constrained system is simply a special case of the Chetaev relation.



Numerical calculation of local resistance coefficient  of cylindrical tube with sudden shrinkage

LIU Lili1, 2, YANG Hanxiao1, 2, WANG Qing3, TAO Congying1, 2, Hong Li1, 2

College Physics. 2026, 45(2):  23.  doi:10.16854/j.cnki.1000-0712. 250320

Abstract ( 24 )   PDF (582KB) ( 10 )  

Related Articles | Metrics

In the undergraduate textbook of Engineering Fluid Mechanics, the calculation of the local resistance coefficient of the cylindrical pipe with sudden shrinkage is given by the empirical formula, which only considers the influence of sudden shrinkage ratio on the local resistance coefficient, which is deviated from the actual situation. Therefore, in this paper, the factors affecting the local resistance of the pipe are analyzed by fluid mechanics theory and numerical calculation method. The research results show that the local resistance coefficient of the pipe is positively correlated with Reynolds number and relative roughness, which provides a basis for the correction of the local resistance coefficient formula of sudden shrinkage pipe.



Application of CBLP Teaching Method in Science& Engineering Courses —Taking “Thermodynamics” as an Example

QU Bo

College Physics. 2026, 45(2):  26.  doi:10.16854/j.cnki.1000-0712.250509

Abstract ( 35 )   PDF (665KB) ( 17 )  

Related Articles | Metrics

As a teaching method based on practical examples, casebased teaching has been widely adopted and achieved significant results in the humanities and social sciences. However, its application in core foundational courses in science and engineering remains in the exploratory stage. This study takes the course “Thermodynamics” as an example to systematically explore the theoretical foundations, practical approaches, and teaching outcomes of the CaseBased Learning for Physics (CBLP) teaching method in undergraduate foundational courses in science and engineering. By designing a series of typical thermodynamics problem cases, the teaching process guides students to first analyze the cases and independently explore solutions, then systematically learn relevant theoretical knowledge, and finally return to the cases for verification and extension, forming a complete teaching cycle of “casetheoryapplication. ” Teaching practice demonstrates that the CBLP teaching method can effectively enhance students learning initiative, critical thinking, and knowledge application abilities. This study further analyzes the challenges faced during the implementation of the CBLP teaching method and proposes corresponding solutions, providing practical evidence and theoretical reference for the broader application of the CBLP teaching method in foundational science and engineering courses．



The exploration and practice of improving the contribution of college  physics course to practical combat teaching——Taking “the Doppler effect” as an example

ZHOU YA-ling, LIU Yang, YANG Fan, ZHANG Jian-qiao, WANG Zhong, XIA Bin, CHENG Shi-hui

College Physics. 2026, 45(2):  31.  doi:10.16854/j.cnki.1000-0712.250224

Abstract ( 36 )   PDF (1084KB) ( 22 )  

Related Articles | Metrics

To effectively implement the military education policy for the new era, the college physics teaching in military academies must highlight actual combat. Combining the development positioning, concepts, and curriculum characteristics of military academies, this article takes the classroom teaching practice of the Doppler effect as an example to focus on practical combat applications. Using military weapons and equipment as the main thread, it proceeds from the surface to the principle and then from the principle to actual combat, exploring the approaches and methods for integrating college physics curriculum teaching with military affairs. It transforms the classroom into a battlefield, highlighting the military and political characteristics of college physics curriculum teaching. Practices have shown that this teaching design has significantly consolidated the foundation of trainees' job capabilities, made great contributions to the actual combatization of trainees, and it has met the requirements of cultivating people with virtue and educating people for war.



Design of digital courseware for physics teaching using JavaScript

HE Zhuo-ran, DING Yi-min

College Physics. 2026, 45(2):  35.  doi:10.16854/j.cnki.1000-0712.250168

Abstract ( 27 )   PDF (713KB) ( 12 )  

Related Articles | Metrics

Digitalized physics teaching is flourishing and now covers multiple generations of technologies such as multimedia, virtual simulation, artificial intelligence, as well as various device platforms such as computers and mobile phones. As a dynamic webpage scripting language, JavaScript has advantages such as light-weight coding, strong interactivity, excellent platform compatibility and portability. We use JavaScript to develop several digital physics-teaching coursewares, pursuing the constructivistic ideals of situational, exploratory, and heuristic teaching. This new technology runs through the entire process of ETA physics teaching to continuously enhance students’ ability to connect theory with practice and creativity in theoretical, experimental classes, and daily life.






Study on the impact of extended content on the teaching effectiveness of #br# measuring liquid nitrogen’s specific latent heat of vaporization experiment#br#

JIN Yuan-wei, PAN Wei, ZHAO Xi-mei, GU Ruo-xi

College Physics. 2026, 45(2):  39.  doi:10.16854/j.cnki.1000-0712. 250127

Abstract ( 20 )   PDF (695KB) ( 6 )  

Related Articles | Metrics


（National Experimental Teaching Demonstration Center, School of Physics and Astronomy, 
Shanghai JiaoTong University, Shanghai 200240, China）

Abstract: In the experiment of “Measuring the specific latent heat of vaporization of liquid nitrogen” in the Physics Experiment II for engineering students, there are several issues, such as the simplicity of the curriculum content, low utilization rate of class hours, insufficient cultivation of students′ innovative thinking, and excessive explanation of data processing software. To address these problems, we introduce extended content such as LabVIEW programming, the differential method for measuring the specific latent heat of vaporization of liquid nitrogen, and the mixing method for measuring the heat released by a copper column in groups. A questionnaire survey is conducted among 149 engineering students regarding their experimental experiences. The results show that the mixing method for measuring the heat released by a copper column is appropriately challenging and rich in physical concepts. It not only ensures the satisfaction of experimental teaching but also enhances the hierarchy of the experimental content, which helps students to gain a deeper understanding of the experiment and significantly improves their experimental performance.
Key words: liquid nitrogen’s specific latent heat of vaporization; extended content; teaching effectiveness





Teaching reform in college physics under the guidance of curriculum #br# ideological and political education: A practical exploration#br#

WANG Fei, YU Yongqin, JIANG Changyong

College Physics. 2026, 45(2):  44.  doi:10.16854/j.cnki.1000-0712.250225

Abstract ( 32 )   PDF (684KB) ( 13 )  

Related Articles | Metrics

To address three major challenges in physics education—students focus on repetitive problem-solving at the expense of true understanding, reluctance to ask questions resulting in the accumulation of unresolved issues, and diverse academic foundations making it difficult to meet all learning needs—innovative reforms are introduced into the college physics curriculum. Guided by the principles of integrating ideological and political education into the curriculum and adopting a student-centered approach, the reforms incorporated strategies such as exploring classical physics texts to emphasize the process of concept introduction, caring for students psychological well-being while encouraging inquiry-based learning, and implementing tiered management of knowledge according to students’ varying academic foundations. Through multiple rounds of practice, the effectiveness of these reforms is validated by improvements in student evaluations, academic performance, and engagement in consultations. The study further highlights the crucial role of one-on-one, appointment-based tutoring in supplementing classroom instruction: it enables intelligent scheduling, respects students privacy, fosters active inquiry, and allows instructors to gain an accurate understanding of students learning status, thereby supporting more targeted teaching improvements. A continuing challenge for future work is how to motivate students with weaker foundations to participate more actively in the questioning and learning process.






Construction and implementation of WeChat official accountassisted optics teaching model#br#

HONG Xuhai, YANG Yulin

College Physics. 2026, 45(2):  50.  doi:10.16854/j.cnki.1000-0712.250276

Abstract ( 25 )   PDF (954KB) ( 9 )  

Related Articles | Metrics

In order to thoroughly implement the national digital education strategy and innovate the teaching mode, this study takes the optics course as the practice carrier to systematically explore the teaching auxiliary function of the WeChat official account. Through the longterm teaching practice, the basic framework of teaching resource library of WeChat official account has been constructed. Based on the platform operation data and user research, the key elements of resource construction are analyzed in depth, and an efficient digital learning platform is created. The research shows that the model has achieved remarkable results in promoting the digital transformation of higher education, optimizing teaching methods and improving teaching quality, which provides a practical example for teaching reform and innovation.



Einstein in the history of quantum physics in the 20th century#br# (2) Competition with Hilbert—from Poisson equations to gravitational field equations#br#

ZHAO Songnian1, YU Yunxian2, WANG chuan3

College Physics. 2026, 45(2):  55.  doi:10.16854/j.cnki.1000-0712.250099

Abstract ( 24 )   PDF (1178KB) ( 19 )  

Related Articles | Metrics

 This article discusses a puzzling problem in the history of physics, that is, Einstein almost struggled to explore the gravitational field equation for nearly eight years, but Hilbert was able to reach the end of the race to establish the gravitational field equation almost simultaneously after listening to Einstein’s six relevant reports. Naturally, there is a difference between thinking about gravity in physics and thinking about gravity in mathematics, or in the way physicists and mathematicians approach and deal with gravity. Their deep thinking and analysis of Poisson's equation obtained important inspiration from it, and thus established the correct idea of establishing their own gravitational field equation. However, if one thinks deeply, it is natural to ask whether there are other academic viewpoints and lines of inquiry that prevent Einstein from thinking smoothly about gravity. Undoubtedly, this is a scientific community worthy of deep thought and discussion. In order to compare, this paper gives the whole process of deriving the equations of gravitational field from the physical concept of Einstein and from the variational theory of Hilbert. When it comes to tensor, a mathematical tool, the paper gives a simple, clear and conceptual discussion. In order to improve readability, the novel diagram from vector to tensor drawn by the author is attached. The author believes that readers who have read this article will certainly have a deeper understanding of the gravitational field equation of general relativity, the variational method and the relationship between tensor and vector; You will also gain insight into the different research styles and creative modes of two famous scientists, Einstein and Hilbert.



Visualization study of hydrogen atom systems under relativistic conditions

LUO Yue, YUAN Dandan, WANG Xingyu, HUI Chunfeng, HUANG Yue, SHU Song

College Physics. 2026, 45(2):  65.  doi:10.16854/j.cnki.1000-0712.250253

Abstract ( 15 )   PDF (2303KB) ( 9 )  

Related Articles | Metrics

 This paper focuses on the relativistic hydrogen atom system. Starting from the Dirac equation, the relativistic wave function of the electron of the hydrogen atom is strictly solved. On this basis, the MonteCarlo simulation method is adopted to sample the probability cloud density of the electron, and the threedimensional visualization of the probability cloud of the electron with spin in the hydrogen atom under relativistic conditions is realized by using Mathematica software. The electron cloud distribution under different principal quantum numbers, orbital angular momentum quantum numbers and magnetic quantum numbers is analyzed, and the electron cloud morphology under relativistic and non-relativistic conditions is compared. In addition, this paper proposes a probability cloud sampling algorithm based on the acceptance rejection sampling method, which can be effectively applied to the visualization of the electron cloud of general atomic systems with spin.







Discussion on the peak frequency and peak wavelength of blackbody radiation#br#

YAO Lewei1, 2, SU Wei1

College Physics. 2026, 45(2):  73.  doi:10.16854/j.cnki.1000-0712.250321

Abstract ( 18 )   PDF (541KB) ( 25 )  

Related Articles | Metrics

The study of blackbody radiation has not only promoted the development of thermodynamics but also directly led to the emergence of quantum mechanics. A blackbody at a temperature above absolute zero can radiate electromagnetic waves. For electromagnetic waves, the product of frequency (ν) and wavelength (λ) equals the speed of light c. Wiens displacement law states that the product of the peak wavelength of blackbody radiation and temperature equals Wiens constant. However, deriving from Plancks blackbody radiation law reveals that the product of the peak frequency and peak wavelength is approximately 0.568 times the speed of light, not c. To address this counterintuitive result, we examine the differences and connections between the definitions of blackbody radiation power expressed in terms of frequency and wavelength, thereby elucidating this counterintuitive issue.




Mathematical and physical analysis of phase jump in electromagnetic waves

ZHNAG Zhan, XING Shuya, WU Dan, ZHOU Wenping

College Physics. 2026, 45(2):  77.  doi:10.16854/j.cnki.1000-0712.250273

Abstract ( 16 )  

Related Articles | Metrics

In this paper, based on the separation of variables method from mathematical physics equations, we derive the Fresnel equations from Maxwell’s equations and the boundary conditions at dielectric interfaces. Then using contour plots of the reflection (transmission) coefficient’s modulus and argument vs. relative index of refraction and incident angle, we systematically analyze the conditions for half-wave loss in reflected waves and additional optical path differences in thin-film interference problems. This work underscores the intrinsic link between optics and methods of mathematical physics, serving to stimulate students’ interest in comprehensively applying their knowledge.






Effect of growth temperature on the crystalline structure and magnetism of Y3Fe5O12

CHEN Zhe1, DAI Yu1, YANG Mengmeng1, 2

College Physics. 2026, 45(2):  83.  doi:10.16854/j.cnki.1000-0712.250415

Abstract ( 27 )   PDF (692KB) ( 9 )  

Related Articles | Metrics

Crystal structure is a key teaching point in the solid state physics course, and growth temperature plays a crucial role in the crystal fabrication process, determining the quality of crystals. During teaching, students often struggle to understand the relationship between the microscopic structure of crystals and their macroscopic properties. This paper prepared a series of Y3Fe5O12 (YIG) films at different growth temperatures using magnetron sputtering, systematically studying their crystal structure and magnetic properties. Experimental results show that YIG can crystallize to form single-crystal films above 150 ℃, with films grown at 200 ℃ exhibiting the smallest damping factor (0.8 × 10-3). This work not only provides a reference for YIG preparation but also consolidates students understanding of crystal structure concepts and deepens their comprehension of explaining macroscopic physical properties from a microscopic perspective.






Atomic magnetometer based on optical pump magnetic #br# resonance amplitude frequency response#br#

ZHANG Yukun1, HU Youran1, ZHANG Chen2, GUAN Xiangze2, ZHANG Feixiang3, LI Chen1, CHEN Chang#1, WANG Zhiguo2

College Physics. 2026, 45(2):  87.  doi:10.16854/j.cnki.1000-0712.250330

Abstract ( 28 )  

Related Articles | Metrics

This paper presents the design and fabrication of a weak magnetic field measurement instrument based on optical pumping magnetic resonance frequency-amplitude response. The instrument employs a sweep frequency method for measuring weak magnetic fields, offering a simple and intuitive approach with a wide measurement spectrum. A phase-locked amplifier is used to implement the sweep frequency, with the sweep frequency interval set to drive the coil and generate the sweep magnetic field. The AD module of the DSP28335 development board is utilized to achieve signal phase-locked amplification and data acquisition/analysis. A PID temperature control system was designed using the DSP28335 and hardware components, with a reasonable structural design for the apparatus. Analysis of the experimental results showed a small relative measurement error, and the apparatus is easy to operate and adjust. This system can stably measure weak magnetic fields at the μT level, and can basically meet the teaching requirements for weak magnetic field measurement experiments in university physics courses.



Mach-Zehnder interferometric temperature sensor based on a Novel Vernier effect

LI Jiayu1, KONG Yihe1, SU Xinyang1, YANG He2

College Physics. 2026, 45(2):  94.  doi:10.16854/j.cnki.1000-0712.250310

Abstract ( 20 )   PDF (689KB) ( 11 )  

Related Articles | Metrics

A novel fiber-optic temperature sensing scheme based on the Mach-Zehnder interferometer (MZI) is proposed to overcome the interference limitation caused by moiré fringes in conventional interferometric measurements, achieving higher measurement accuracy. The scheme constructs a vernier structure in which interference fringes serve as the primary scale and moiré fringes as the secondary scale, transforming moiré fringes from a source of interference into a tool for enhancing measurement precision. Experimental results show that the designed sensor achieves a linearity of 0.911 (R2) and a minimum temperature resolution of 0.03 ℃, with a fourfold improvement in measurement accuracy compared to traditional single-count interferometers. With its intuitive principle and ease of implementation, this approach holds promise as an ideal platform for educational demonstrations, helping students gain deeper insights into interference principles and the vernier effect while fostering research interest.






Efficient exploration of physical formulas based on artificial intelligence symbolic regression: taking Balmer’s formula as an example

LV Tie-yu, Wu Shun-qing

College Physics. 2026, 45(2):  98. 

Abstract ( 16 )   PDF (692KB) ( 12 )  

Related Articles | Metrics

Science discovery empowered by artificial intelligence (AI) demonstrates remarkable potential in reshaping the paradigm of modern scientific research. Deeply integrating AI tools into physics teaching is of great significance for cultivating innovative research capabilities. Taking the discovery process of the Balmer formula for the hydrogen atom as a teaching case, this paper employs symbolic regression technology to re-explore physical laws in the era of intelligence. By constructing the original experimental dataset of the Balmer series and combining it with the Feyn symbolic regression tool, the entire process of reconstructing the characteristic formula from limited spectral data is systematically demonstrated. The research highlights the principle of “dual-driven by the quantity and quality of data” and reveals the complementary relationship between “mathematical discovery” and “physical interpretation” under the human-machine collaboration model. While AI can accelerate the induction of mathematical laws, the physical interpretation behind formulas still relies on the wisdom of scientists. This case empirically reveals the effectiveness of AI tools in accelerating the induction of mathematical laws. At the same time, it more prominently demonstrates the key supporting role of physical thinking in guiding the iteration of the model, providing a useful idea for the innovation of physics education empowered by intelligent technology.



Innovative experimental instrument based on liquid-core cylindrical lens

MENG Weidong1, 2, GENG Bolin1, 2, PU Xiaoyun1, 2

College Physics. 2026, 45(2):  104.  doi:10.16854/j.cnki.1000-0712.250254

Abstract ( 20 )   PDF (812KB) ( 6 )  

Related Articles | Metrics

This paper presents an innovative experimental instrument using a liquid-core cylindrical lens. The instrument aims to enhance university-level experimental teaching, scientific research, and student innovation in optical measurement applications. Based on a self-designed liquid-core cylindrical lens, the instrument combines methods like the equal-refractive-index thin-layer movement, Boltzmann-Matano, and transient image analysis to achieve rapid, high-precision measurement of liquid refractive indices and liquid-phase diffusion coefficients. Experimental results show that the instrument offers a refractive index measurement accuracy of over 0.0002 RIU and a liquid-phase diffusion coefficient measurement deviation of under 0.02×10-5 cm2/s. It also provides strong anti-interference, short measurement time, and a visual process. Fifteen supporting experimental courses have been developed. These enable students to dynamically observe and numerically simulate processes from optical path adjustment and eliminating spherical aberration to diffusion and dissolution. The instrument is a highly efficient and reliable tool for scientific research and teaching and has broad application prospects.




Construction and implementation of intelligent course in university  physics based on knowledge map

QIU Huaili, SONG Fengquan, LIN Hui, WANG Chunhua, LI Hongju, CHEN Bing, LI Zhongjun

College Physics. 2026, 45(2):  108.  doi:10.16854/j.cnki.1000-0712.250239

Abstract ( 29 )   PDF (713KB) ( 16 )  

Related Articles | Metrics

 In the context of artificial intelligence and higher education, this study explores the construction and implementation of intelligent courses in university physics. The research is based on knowledge graphs and adopts a hybrid teaching mode that combines online and offline methods, aiming to address the autonomous and personalized learning needs of students in the digital and AI era, as well as the requirements of the new engineering construction for the cultivation of advanced abilities in university physics general courses. By constructing a intelligent course teaching system and implementing teaching strategies such as problem oriented, project-based, and seminar based, combined with course specific intelligent agents to optimize students learning experience, and using big data to analyze students learning trajectories, personalized learning paths are recommended. Teaching practice has shown that the construction of smart courses has significantly improved students learning effectiveness, the overall improvement in mid-term and final grades in the past five teaching semesters is significant. The research conclusion shows that the construction and implementation of intelligent courses based on knowledge map and AI technology can effectively improve teaching efficiency and effectiveness, providing useful practical references for higher education reform in the new era.



Exploration of ideological and political education in college physics under  the objective of building armed forces

MIAO Qi, LI Sai

College Physics. 2026, 45(2):  113.  doi:10.16854/j.cnki.1000-0712.250260

Abstract ( 24 )   PDF (629KB) ( 29 )  

Related Articles | Metrics

Guided by the military education policy of the new era, based on the requirements for training military aerospace talents under the objective of building armed forces, adhere to the integrated design of “objective-content-method-evaluation”, we construct an ideological and political education system for college physics that combines disciplinary characteristics and military attributes. This system establishes the ideology and politics education goals that cover three dimensions including the political belief, scientific literacy, and military mission, six thematic ideological and political resources, methods of ideological and political education under the mixed teaching mode, and an assessment system including process evaluation, stage evaluation, and continuous evaluation，a mode of ideological and political education that accompanies the whole process has been formed. The system and education mode have positive significance for cultivating new-era military talents who shoulder the mission of strengthening the military.