热力学与统计物理

The core task of this step is to select an interesting physics problem and establish the corresponding physical model, laying the foundation for subsequent theoretical analysis and experimental verification. Choose specific research questions from the core content of the course, which can be practical problems in classical mechanics, electromagnetism, quantum mechanics, thermodynamics, or experimental physics. Through reasonable approximations and assumptions, abstract practical problems into solvable physical models.

• Select specific physics problems from course content, clarify research objectives and physical significance, which can be theoretical derivation, experimental measurement, or numerical simulation problems
• Review relevant textbooks and literature (APS, IOP, arXiv, Chinese Physical Society journals) to understand the research background and existing results of the problem
• Establish physical model: according to research objectives, grasp main factors, ignore secondary factors, make reasonable approximations, and establish clear physical pictures and mathematical models

The core task of this step is to use fundamental laws of physics and mathematical methods to conduct theoretical analysis and analytical solution of the established physical model. Starting from basic principles (such as Newton's laws, Maxwell's equations, Schrödinger equation, laws of thermodynamics), obtain quantitative relationships between physical quantities through mathematical derivation. Theoretical analysis is the core of physics research, requiring clear physical pictures and rigorous mathematical derivation.

• Establish basic equations: according to the physical model, apply corresponding physical laws (Newtonian mechanics, Lagrangian/Hamiltonian formalism, Maxwell's equations, Schrödinger equation, etc.) to establish governing equations
• Analytical solution: use mathematical methods such as calculus, linear algebra, differential equations, complex functions to try to obtain analytical solutions of the problem, and analyze the physical meaning of the solutions
• Special cases and limit verification: verify the rationality of analytical results through special cases, limit situations, or dimensional analysis, and check whether results conform to physical intuition and known conclusions

The core task of this step is to verify theoretical results or solve problems that cannot be analytically treated through numerical computation and computer simulation. Numerical methods are important tools in modern physics research, including finite element, finite difference, Monte Carlo, molecular dynamics and other methods. Through numerical simulation, physical processes can be intuitively displayed, and the correctness of theoretical predictions can be verified.

• Select numerical methods: choose appropriate numerical methods according to problem characteristics (such as finite difference method, finite element method, Monte Carlo method, molecular dynamics simulation, etc.)
• Programming implementation: use Python (NumPy, SciPy, Matplotlib), MATLAB, COMSOL or other professional software for numerical computation and simulation, and write calculation programs
• Result verification: perform convergence tests and grid independence verification, compare numerical results with analytical solutions or experimental data, and verify the accuracy and reliability of numerical methods

The core task of this step is to design and complete physics experiments, verify theoretical predictions through experimental measurements, or discover new physical phenomena. Experimentation is the foundation of physics, requiring scientific experimental design, standardized operation, and rigorous data analysis. Systematically learn error analysis and data processing methods to ensure the reliability of experimental results.

• Experimental design: design experimental schemes according to research objectives, select experimental instruments and measurement methods, develop experimental procedures and data recording tables, consider error sources and reduction measures
• Experimental operation: operate according to experimental specifications, calibrate instruments, perform multiple measurements to reduce random errors, and record all raw data and experimental conditions
• Data processing: use Origin, Python or MATLAB for data processing and error analysis, calculate uncertainty, draw experimental curves, and compare experimental results with theoretical predictions

The core task of this step is to conduct in-depth physical discussion of research results and write a standardized physics research report. Combine theoretical analysis, numerical simulation, and experimental results to comprehensively explore the essence and laws of physical phenomena. The research report must conform to physics academic standards, with clear physical pictures, standardized data charts, and rigorous argumentation logic.

• Result discussion: in-depth analysis of theoretical and experimental results, explain physical mechanisms, discuss physical significance and scope of application of results, analyze error sources and influencing factors
• Report writing: write the report according to physics paper standards, including abstract, introduction, theoretical methods, experimental/computational results, discussion, conclusions, references, using standard physics terminology
• Summary and outlook: summarize main findings and innovations of the research, compare advantages and disadvantages of different methods, and propose improvement directions and future research ideas