The Jaynes-Cummings (JC) model is one of the most fundamental models for the interaction between light and matter. In this paper, we first derive the explicit expression for the time evolution operator of the JC model when the light field resonates with a two-level atom. Based on this, we calculate the analytical expressions for the system state and the population of each atomic energy level as a function of time when the two-level atom is initially in a superposition of two energy eigenstates and the light field is in a superposition of three photon number states and a coherent state, respectively. Finally, this paper introduces QuTiP, a useful extension library in Python for quantum mechanics simulation and numerical solution, and uses it to numerically solve the time evolution of this model, obtaining results consistent with the analytical solutions. These computational processes are of great significance in scientific research and university physics teaching.

This article examines the resolution of a problem in thermodynamics and statistical physics, demonstrating the derivation of physical processes under the standard dimension analysis, and presenting results in a standard form. The paper provides a brief elucidation of the Π theorem and furnishes examples of dimensional analysis employing the Π theorem for physical systems. Given the significance of dimensional analysis in physics, it warrants ample emphasis in the instruction of foundational physics courses. Additionally, the appendix of the paper offers standard representations of formulas sourced from the sixth edition of “Thermodynamics and Statistical Physics” written by Wang Zhi-Cheng.

The Coulomb interaction satisfying the inverse square law has unique significance in the field theory, the Gauss's theorem and describes the source property of the three-dimensional vector field. In this paper, other types of potentials such as Yukawa potential and harmonic oscillator potential are transformed into equivalent Coulomb charge distribution in the space. Therefore, the Gauss's theorem can be applied to calculate the field strength and other related physical quantities. An example of hard sphere scattering with uniform distribution of Yukawa charges is designed to show the advantages of this method. Although no significant improvement on the calculation workload, the equivalent Coulomb charge distribution has a clearer physical picture when dealing with the sizable particles. The conversion method and the specific examples can be used for reference to expand the teaching of field theory and related courses.