With the help of Zerilli variable，the linearised Einstein equation can be reduced to a simple second order wave equation，from which we solve the quasi-normal frequency routinely. However，if we try to calculate the perturbed metric them selves，we need to do one extra time integration and many spatial differentials on the power serial form master variables. This forms heavy burden for the second order perturbation calculation. This paper takes the perturbation metric components themselves (either one of the three) as master variables and derives out their differential equations directly，which are spatially differentiated three times and temporarily differentiated twice. We solve this equation by the usual power serial method and get quasi-normal frequencies coincident with those solved out from Zerilli equation，thus we establish an equivalences between the two methods and making much advantageous preparation for higher order perturbations calculation.

 In order to improve the complicated pose adjustment and operation steps involved in the experiment of measuring the top angle of the prism by spectrometer，optimize the structure space of the device and improve the measurement efficiency，a double-mirror reflection method is proposed. In this method，the laser as the light source is vertically incident on the bottom surface of the prism and refracted on the slope of the prism. The refracted light is reflected several times between the two parallel mirrors and received by the target surface of the CCD detector to form a laser spot，and the center position of the spot S1 is recorded. Rotate the prism by a known small angle β，at which time the light spot shifts，record the center position of the light spot after the shift S2，and calculate the displacement ΔS between S1 and S2. Finally，the angle β，the displacement ΔS and the measurement formula are used to calculate the top Angle a. The experimental results show that when the interval of two mirrors is between 65 mm and 95 mm，and the rotation Angle β is selected between 0.1° and 0.2°，the measurement error between the measured top Angle a of the prism to be measured and the standard value is less than 0.25%. This method doesnt involve complex telescope adjustment in the spectrometer. It not only folds the system optical path，reduces instrument weight，and optimizes device space，but also has high repeated measurement accuracy by using the double mirrors and an automatic reading program interface with a CCD camera.

Strengthening the teaching workforce is the cornerstone of the education system. In February 2023，the Working Committee for Teacher Education of the Higher Education College Physics Curriculum Guidance Committee，under the Ministry of Education，initiated a large-scale survey on the "current status of secondary school physics teachers in china." The survey encompassed 31 provinces and garnered 11,851 valid questionnaires，which primarily centered on the teacher workforce structure，recognition of the teaching profession，evaluation of college physics courses，and the primary challenges confronting secondary school physics teachers. This study unveiled the following findings: Some teachers still exhibit relatively low levels of recognition for the teaching profession; Regional disparities persist in the development of the teacher workforce in China，with significant distinctions between the western and eastern regions; Some facets of college physics education lack inspiration and fail to cultivate students' problem-solving awareness; Prominent issues include students' weak foundation in physics and a lack of high interest in the subject.

Group theory is a crucial component of physics teaching，with permutation groups being central to discrete group instruction. The concept of groups is profound and complex，and traditional symbolic and matrix-based representations used in teaching are often not intuitive. This makes it difficult for beginners to grasp the core concepts of group theory. Therefore，there is a necessary for a more intuitive and enlightening method in group theory education to help beginners more easily understand fundamental group-related concepts. In this paper，we introduce an alternative symbolic representation called Stick notation，focusing on the example of the 3-order permutation group. These symbols can intuitively demonstrate essential concepts such as group action，conjugation，commutativity，subgroups，and invariant subgroups. This new and engaging tool has the potential to significantly enhance the effectiveness of group theory education.

 By analyzing the dynamic reaction force of water flow，the motion differential equation of the rotary watering sprinkler is established. The critical ejection angle and the critical flow velocity are determined，and it is proved that the unique steady motion of the system is asymptotically stable in a wide range. On this basis，the shape and the irrigation area of the sprinkler are given. Finally，the influence of periodic water flow pulsation is discussed.

In quantum mechanics, studying the evolution of wave packets can help students correctly establish physical images of microscopic particle motion and understand the differences between quantum physics and classical physics. However, the complex mathematical results obtained from solving the Schrödinger equation often make it difficult for students to intuitively understand the evolution laws of wave packets. This article takes the evolution of an electronic wave packet in a magnetic field as an example to introduce how to design visual numerical experiments in teaching practice, in order to visually display the evolution of this wave packet and help students establish a clear physical image of the motion of microscopic charged particle in magnetic field. During this process, various forms such as teacher guidance, student personal participation in the visualization process, classroom flipping, and centralized discussion are combined to effectively enhance students' learning participation and achieve diversified teaching goals.

 To determin the analytical solutions of electromagnetic field and wave in and out of two-wire transmission lines transmitting analog signal，electromagnetic field and wave in and out of two-wire transmission lines is analysed and calculated based on maxwell equation from the angle of TEM wave，TM wave and TE wave in this paper.The results show that TM wave is transmitted in and out of two-wire transmission lines. The analytical solutions of electromagnetic field and wave in two-wire transmission lines consist of zero and 1st-order complex variable bessel functions，the analytical solutions of electromagnetic field and wave out of two-wire transmission lines consist of zero-order complex variable bessel functions and 1st-order complex variable Neumann functions，the relationship between electromagnetic field coefficient and electric current is given in this paper.The results further support for fitting calculation，simulation，signal distortion，electromagnetic compatibility analysing.

According to the characteristic of δ function, it can be treated as the limits of some distribution functions. A few of such functions are given. From these functions, δ function potential can be treated as the limit of square-well potential and the square of sech function potential. The bound state problem of these potential can be solved exactly. The bound state energy and eigenfunction of δ function potential are exactly the limit of corresponding results of these potentials.

 In this work，the thermodynamic probability problem of N gas molecules distributed in the left and right halves of a rectangular container is rigorously solved using the exact form of Stirlings formula，which quantitatively verifies Boltzmanns statistical interpretation of the microscopic nature of the second law of thermodynamics. It is shown that 95% of the total microscopic states are distributed in the ±Ninterval near the equilibrium state，i.e.，the relative fluctuations are 1/Nwith respect to N. Confusion and errors caused by the common Stirling approximation are discussed.

This article takes the systematic errors in the "Verification of Boyle's Law" DIS experiment as the object, explores the sources of error, and proposes four methods to reduce systematic errors, including "compensation volume method", "increasing volume method", "oil sealing method", and "push-pull improvement method". During the process of scientific exploration, it aims to cultivate students' Problem Evidence Awareness and scientific demonstrating ability. The experimental design scheme and teaching ideas proposed in the article can used to cultivate students' scientific thinking, scientific inquiry, and scientific spirit, ultimately improving their problem-solving ability.

The introduction of mature scientific research results into experimental teaching can effectively maintain the advanced and sustainable development of experimental teaching, which has become one of the hot spots of practical teaching reform. Here, the high-speed physical random number generation are introduced into optoelectronic experiments, where the broadband chaotic signal with high uncertainty and high complexity are used as the physical entropy source of high-speed physical random numbers, utilizing semiconductor laser with optical feedback. The experiment involves a wide range of courses and the combination of software and hardware, which can fully exercise students experimental skills and cultivate students sense of innovation and scientific spirit.

 New engineering talents are crucial in addressing the complex challenges of the future world, and the number of such talents determines the overall progress of society. The cultivation of new engineering talents requires innovative teaching design as the cornerstone. Aligned with the connotations of new engineering talent, the educational reform practice based on the Problem-Based Learning (PBL) method, conducted in large-class composed of general students, has considered the beneficial needs of students at various levels, compensating for the scarcity of teaching staff in large-scale class settings. This teaching practice has promoted the deep learning of ordinary students, expanded the beneficiary group of teaching reform, effectively achieved the goals of value shaping, knowledge imparting, and capability cultivation, and the course teaching has a distinct high-level, innovative, and challenging nature, exploring an effective new path for the cultivation of new engineering talents.

 Using Brownian motion as an example, this paper visually and quantitatively explains core concepts of statistical physics such as randomness and thermal motion in fluid by utilizing modern tools. The teaching design is based on the backtracking teaching method, emphasizing the overall construction of the theoretical system. Through the stages of introduction, retroaction, learning, practice, thinking, and application, innovative thinking ability is cultivated throughout the entire process of college physics experiment teaching. By developing teaching instruments for widespread use, classical physics experiments are replicated and expanded upon to deepen students’ understanding of finding, raising, analyzing and solving problems as well as the complete chain of scientific research from practical experience. This approach enhances students’ innovative thinking ability, and overall scientific literacy while maximizing the effectiveness of experimental teaching.

Solid state physics is a course that closely follows the forefront of scientific research, but it contains a large number of abstract physical concepts and complex derivation of physical formulas. Students face problems such as a lack of clear physical images and insufficient participation in learning. This article attempts to integrate

This article analyzes in detail the total work done by the microscopic sliding friction forces at the bottom of the small ball in an infinitely small time, and obtains the expression of the elementary displacement of the point of action of the macroscopic sliding friction force. It is pointed out that the action point is a hypothetical concept when the work is done. The actual sliding distance of the small ball is obtained by integration, and the total work done by all sliding friction forces is calculated. It is pointed out that the distance of the small ball sliding plus the distance of the small ball rolling is equal to the displacement of the center of mass of the small ball. It is also pointed out that the sliding and rolling of the small ball are carried out simultaneously rather than alternately. It is proved that, formally, the negative work done by the sliding friction force on the entire displacement of the center of mass of the small ball leads to the decrease of the translational kinetic energy of the small ball, while the positive work done on the reverse rolling distance leads to the of increase in the rotational kinetic energy of the small ball. The main purpose of the article is to reveal the mechanisms of the work done by the sliding friction force acting on a small ball sliding and rolling on the ground.

The spherical pendulum is a single pendulum that rotates around the suspension point under the action of gravity, and hence its center of mass is constrained on a sphere. In this paper, we numerically simulate the motion of a single spherical pendulum, and discuss the dependence of the swing period on the initial conditions. By the numerical analysis of the dynamics of the coupled spherical pendulums, we show the influence of the spring stiffness on the energy transfer, discuss the frequency distribution of the energy, and clarify the chaotic state of the nonlinear large swing angle motion.

This paper introduces the extensive application of Bessel functions, a core topic in mathematical physics courses, at the forefront of research in gravitational wave physics. We focus on the significance of Bessel functions through a detailed discussion using the example of gravitational wave radiation from cosmic strings.  Additionally, we briefly outline their application in higher-order mode gravitational wave radiation from binary systems and gravitational waves from phase transitions. This study can serve as an example of educational reform integrating undergraduate core curriculum teaching with undergraduate research.

When the mirror rotates within the incident plane, the angle change of the reflected light is twice the mirror's rotation angle. However, when the mirror rotates out of the plane, the angle change of the reflected light is difficult to describe quantitatively. This paper combines the law of light reflection and the geometry to study the angle change of the reflected light when the mirror rotates freely in three-dimensional space. A general expression is obtained, which is related to the incident angle, the in-plane rotation angle, and the out-of-plane rotation angle. The results show that when there is no rotation within the incident plane, the angle change of the reflected light varies most rapidly with changes in the out-of-plane rotation angle. As the in-plane rotation angle increases, the angular change of the reflected light with the out-of-plane rotation angle gradually decreases until it reaches zero. These findings enhance the understanding of the behavior of reflected light when the mirror rotates in free space and provide theoretical support for light propagation in fast reflectors, scanning systems, and digital micromirror devices.

In the Newton's ring experiment, the diameter of the circular fringe is the fundamental data of measurement. In order to improve the accuracy of measurement, this article theoretically analyzes the reasons that cause systematic errors: firstly, the diameter does not pass through the center of the circular fringe (introducing different chord-center distances), and secondly, the two endpoints of the chord deviate from the position of the extreme light intensity. So in theory, a new method is proposed to completely eliminate the above errors in Newtons ring experiment: replacing the diameters with the chord length of all circular fringes with equal chord-center distance, and combining the extreme value of light intensity to locate the two endpoints of the chord. Based on this method, two new measurement arrangements are proposed for the Newtons ring experiment: in the case of using a reading microscope, a common chord for all concentric circular fringes can be added to the Newtons ring instrument as a reference line for measuring the chord length of each circular fringe, and the chord length can be used instead of the diameter to eliminate the first systematic error; in the case of image analysis method, the light intensity distribution on the common chord can be further obtained, and by locating the two endpoints of the chord through the extreme light intensity, the accurate length of the chord of all circular fringes can be obtained, thereby eliminating the above two types of systematic errors. Then, the image analysis method is applied to the newly designed Newtons ring device for measurement, proving that this method is effective and feasible.

Vibration is an important topic in classical physics, and resonance phenomena in continuous media correspond to vibrations in a class of eigenmodes. In the undergraduate course “Methods of Mathematical Physics” for physics majors, eigenmodes are introduced in the chapter on “Separation of Variables” while solving eigenvalue problems. However, the abstract formulas and the relatively unfamiliar concept of eigenmodes can be non-intuitive 

Vibration is an important topic in classical physics, and resonance phenomena in continuous media correspond to vibrations in a class of eigenmodes. In the undergraduate course “Methods of Mathematical Physics” for physics majors, eigenmodes are introduced in the chapter on “Separation of Variables” while solving eigenvalue problems. However, the abstract formulas and the relatively unfamiliar concept of eigenmodes can be non-intuitive and difficult to understand for beginners. In this paper, we propose a thin-plate resonance scheme to visually demonstrate this physical phenomenon. This approach is combined with the “Separation of Variables” method for solving eigenmodes presented in the course, thereby producing images that closely resemble those observed in the demonstration experiment. The finite-element software is also employed to simulate these resonance modes and frequencies.

Diffraction is a fundamental phenomenon in optics. Deriving an analytical solution for the diffraction of complex apertures is generally challenging. To obtain the Fraunhofer diffraction patterns of complex apertures, the ear-clipping method is employed to approximate the aperture by dividing it into multiple triangles. Consequently, the total diffraction field of the aperture can be expressed as a superposition of the diffraction fields of these triangles. The Fourier transform of each arbitrary triangle is computed by converting it, through coordinate transformation, into the Fourier transform of a basic right triangle. Subsequently, an experimental setup for Fraunhofer diffraction is constructed to measure the diffraction field distribution for different apertures. The angular distribution uncertainty is calculated to analyze the diffraction field of regular polygonal apertures, verifying the feasibility and accuracy of the proposed analytical algorithm. Finally, the diffraction field of complex fractal apertures is computed and the algorithm's effectiveness in calculating diffraction fields of complex apertures is demonstrated