A double well on-line simulation and activities for active learning of introductory quantum mechanics

Abstract

Teaching introductory quantum mechanics is challenging, especially to students who have limited knowledge of mathematics. The challenges and approaches are evidenced in a wide range of literature. Our goal is to develop an active engagement module for introductory quantum mechanics that would cover the most important concepts: indeterminism, incompatibility, the difference between superposition and statistical mixture and the role of measurement. To accomplish this, we developed a free on-line simulation of a double well—a (pseudo) two-state system—which is able to evidence all of the above concepts. Students perform simulated experiments and build their knowledge from their observations. We present the simulation and the proposed experiments to address the above concepts. We provide a description of the activities and their outcomes as tested with high-school students in different settings. Qualitative analysis of learning outcomes offers evidence that between 60% and 100% of students can reach the following conclusions on their own. (i) The particle is only ever detected in one of the possible states. (ii) The outcome of one experiment cannot be predicted, only its probability can be predicted. (iii) For some pairs of quantities, knowing the value of one quantity exactly precludes the possibility of knowing the value of the other quantity exactly. (iv) A statistical mixture (of eigenstates) is not the same as a superposition state. (v) The measurement affects the time evolution of the system. The most difficult conclusion for students to reach is how exactly the measurement affects the system. The success rates presented here lead us to conclude that the simulated experiments can be very useful when designing an active engagement course on the concepts of quantum mechanics. While the development is done in high-school, we believe the results are also relevant for introductory university level, especially for non-physics students.

Quantum uncertainty: what to teach?

“…The material is based on school experiments with polarisers leading to the verification of Malus' law which is interpreted as the probability of a photon passing through a polariser. Since then, alternative teaching materials also appeared, for instance, studying quantum phenomena related to photon-beam splitter experiments [2], or using a computerbased environment to explore the behaviour of a particle in a simplified double-well potential box [3]. A possible motivation behind these developments is the preparation of secondary school teaching for the age of quantum computers or quantum cryptography [4][5][6], also supported by the choice of topics of The Nobel Prize Committee in Physics 2022 [7].…”

“…Teaching experiments have also been performed showing encouraging positive outcomes [8][9][10][11][12][13]. Teaching materials [1][2][3] are based on Dirac's approach [14] as well as on later textbooks dealing with two-state quantum systems [15][16][17][18], although the mathematics used by them is unavoidably restricted to real numbers and planar vectors. We note that the International Business Machines (IBM) material [4] and a popular textbook on quantum computing [19] illustrate that one can go quite far from a conceptional point of view by the use of only real numbers.…”

“…Teaching materials [1][2][3] establish the probabilistic nature of individual quantum measurements: a measurement can have probabilistic outcome even if ideal instruments are used. Teaching materials apply the term quantum uncertainty to describe the feature that a typical quantum state is a superposition state.…”

Requirements for future quantum workforce – a Delphi study

“…Much more, it is in line with physics education research efforts on quantum physics as different teaching sequences on modern quantum physics in schools and universities have been developed. For example, teaching sequences using the qubit approach [13,14] a quantum optics-approach [15,16,17], haptical approaches [18,19], the double-well approach [20] or presenting characteristic traits of quantum mechanics [21]. With modern advances in quantum technologies, new potentials are now emerging for the teaching of modern quantum physics at all levels.…”

Computer simulations for the teaching of photoelectric effect

“…For engineers, the photoelectric effect allows exploring technological applications such as the operation of lamps, photoelectric sensors, lasers, diodes (Jia, Ma, & Hunter, 2007) and a variety of applications and processes associated with the emission and transformation of V. 19 Nº 1, julho, 2021_______________________________________________________RENOTE DOI: https://doi.org/10.22456/1679-1916.118488 ____________________________________________________________________________________________ light. Because of this, there is a growing interest in introducing quantum mechanics at the pre-university level and for non-physics students (especially engineers) at the university level (Sergej Faletic, 2020).…”