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Physics Education

Teaching the concept of uncertainty principle by simulating wave packet for a localized particle

Iqbal Singh, K Khun Khun

Published Jun 10, 2025• 0 citations
Publisher

Abstract

Abstract Concept of wave packet is one of the most relevant topic of quantum mechanics but teaching it in an abstract way does not enhance the learning of students. On the other hand visualizations make such topics very easy in classroom learning. To capture the attention of students in classroom teaching, a unique way to simulate the wave packet associated with a localized particle is presented in this paper. This work describes an easy method to generate data for tracing a wave packet by organising an excel spreadsheet. This method is simple and aids the understanding wave packet modulation with variation in range of wave vectors of constituents matter waves. The obtained uncertainty product in position and momentum of the particle can be further utilized to verify Heisenberg’s uncertainty principle.

DOI
10.1088/1361-6552/adda87

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Abstract Concept of wave packet is one of the most relevant topic of quantum mechanics but teaching it in an abstract way does not enhance the learning of students. On the other hand visualizations make such topics very easy in classroom learning. To capture the attention of students in classroom teaching, a unique way to simulate the wave packet associated with a localized particle is presented in this paper. This work describes an easy method to generate data for tracing a wave packet by organising an excel spreadsheet. This method is simple and aids the understanding wave packet modulation with variation in range of wave vectors of constituents matter waves. The obtained uncertainty product in position and momentum of the particle can be further utilized to verify Heisenberg’s uncertainty principle.
The objective of this article is to graphically illustrate to the students the Gaussian wave packet and its momentum representation using spreadsheets. Gaussian wave packet with different standard deviations is obtained using interactive spreadsheet. Using Fourier transform the momentum representation is obtained. Using Gaussian wave function and its momentum representation the uncertainties in position and wave number are obtained the uncertainty relation is verified. This will make the concept, which so far is left to the abstract imagination come alive for the student, and initiate a deeper understanding of quantum physics problems.
The Heisenberg uncertainty principle is one of the foundations of quantum mechanics,although meaning of this principle is disputed in the region of physics.The teaching of this principle should help students to discard the conventional conception of orbit and estab lish the idea of wave-particle duality.However,the conventional conception of orbit is still used in many domestic textbooks of university physics.The stude nts tend to be confused consequently.Therefore,tens of textbooks of university physics are investigated and different accounts about uncertainty principle are compared,and then advice of teaching on this principle is brought forward.
Abstract Teaching and learning of quantum physics at secondary level is an active field of research. One important challenge is finding ways to promote understanding of quantum concepts without the mathematical formalism that is embedded in quantum mechanics but unavailable on the secondary level. We investigated Norwegian secondary students’ (N = 291) descriptions of the wave nature of quantum particles and the uncertainty principle, as expressed during work with learning resources using a sociocultural approach emphasizing history, philosophy, and nature of science aspects. Responses from university students (N = 40) given after a formalism-based course in quantum physics were included for comparison. Themes were identified using thematic analysis and analyzed from the perspective of pedagogical link-making, seeing different themes as representing different levels of explanations of the concepts (phenomenological, qualitative, mathematical). The most dominant theme in descriptions of particle wave nature was that particles exhibit wave behavior in experiments, while referring to the mathematical description of particles by wave functions was a less prominent theme, even among university students. Two uncertainty principle themes were found: uncertainty as inability to measure pairs of variables precisely, and uncertainty as innate blurriness in nature. Largely missing from descriptions of both concepts were meaningful links between different levels of explanations. Based on the results, we discuss ways forward for teaching particle wave nature and uncertainty in secondary education.
The Uncertainty Principle is usually discussed twice in a Quantum Chemistry course. The first discussion is a “pre-wave function” explanation that occurs before students know about wave functions, but do know the de Broglie hypothesis. The second description of the Uncertainty Principle is “post-wave function”, i.e., after students have learned about wave functions, operators, and expectation values. The more common pre-wave function explanations of the Uncertainty Principle can lead students to believe that the Uncertainty Principle sets limits upon what can be measured in the lab. This is the “measurement view” of the Uncertainty Principle. The Uncertainty Principle says something much deeper than this; particles do not possess some properties solely because of their wave nature. This is the “particle-centric view” of the Uncertainty Principle. We show that the Uncertainty Principle can be explained from the preferred particle-centric view when students only know about the de Broglie wavelength and basic statistics. To accompany this pre-wave function discussion of the Uncertainty Principle, we have designed an interactive Module that students can use to visualize the Uncertainty Principle from the particle viewpoint. We also describe a way to explain the Uncertainty Principle, which is complementary to the pre-wave function discussion, after the students know about wave functions, using the same elementary statistical analysis used in the pre-wave function presentation. We have designed a second interactive Module that students can use to visualize the Uncertainty Principle when particles are described by complex wave functions.
Abstract Quantum mechanics, the cornerstone of modern physics, is often perceived as abstract and complex, particularly by beginners, with regard to the wave-particle duality of microscopic particles. Traditional teaching methods often fail to foster an intuitive understanding of these concepts among students. Consequently, the search for more effective, interactive teaching tools has become a priority for educators. Our objective is to demystify complex quantum mechanical concepts, spark students’ interest in learning, and deepen their understanding, ultimately improving teaching effectiveness. In our research, we used LabVIEW software to develop a visual display and interactive simulation for double-slit interference and circular aperture diffraction experiments of electrons. This module allows students to simulate these experiments and adjust parameters, providing an intuitive observation of quantum behavior under various conditions. The results indicate that using the LabVIEW multimedia module significantly enhances students’ comprehension and interest in quantum mechanics, particularly with respect to wave-particle duality. We also employed the Feynman path integral idea to explain some of the simulation phenomena. This LabVIEW-based simulation not only renders abstract concepts more tangible and visual but also fosters active learning and experimental investigation. We posit that this study introduces a novel and valuable tool for teaching quantum mechanics and provides insights for the future of quantum mechanics education.