Angular momentum is a difficult knowledge point for undergraduates to understand in quantum mechanics. In this paper, a number of numerical experiments are designed to help students build visual images of angular momentum. The design concept is to break the boundaries between elementary and advanced quantum mechanics, basic theory and cutting-edge research, guide students to calculate and draw by themselves, discuss with each other, and build their own physical pictures. Through this efficient way of learning by doing, students can get an intuitive sense of abstract concepts from some simple calculations. The discussion starts from rotation operation, gradually increases the difficulty to squeezing operation, and introduces the basic concepts of spin squeezed state and Husimi Q representation. This design skillfully links classroom teaching with frontier research, bringing deeper thinking and inspiration to undergraduates.