Eigentheory concepts are central in mathematics and physics; they serve multiple functions, such as symbolizing physical phenomena and facilitating mathematical computations. Words and meanings associated with eigentheory develop and vary over time, as do their associated symbols. In this study, we investigate how "eigen" develops over…

This study aims to give chemistry students a deeper understanding of electron shielding and quantum transitions by interpreting the characteristic X-ray lines. There is a popular misunderstanding among learners and even teachers in which an outer-shell electron fills a vacancy in the inner shell, releasing some of its energy as an X-ray photon.…

The principles of process-oriented guided inquiry learning (POGIL) are applied to the analysis of the emission spectrum of atomic hydrogen. Over the course of three learning cycles, students construct the hydrogen atom's energy level diagram and assign quantum numbers using their measurements of the Balmer series plus additional information on the…

The concepts taught in an undergraduate physical chemistry course are directly related to the molecular processes governing climate change, yet the connections between quantum mechanical molecular properties and global warming are rarely made explicit. To improve student knowledge about climate change, we developed a three-part activity that…

Validated conceptual multiple-choice surveys administered before and after instruction in relevant concepts can be useful tools to gauge the effectiveness of curricula and pedagogical strategies. Here we discuss the use of four different validated surveys to investigate student understanding: The Energy and Momentum Conceptual Survey (EMCS), the…

We report an educational tool for the upper level undergraduate quantum chemistry or quantum physics course that uses a symbolic approach via the PySyComp Python library. The tool covers both time-independent and time-dependent quantum chemistry, with the latter rarely considered in the foundations course due to topic complexity. We use quantized…

Simple mathematical models can serve to reveal the essence of experimental phenomena and scientific concepts. The particle in a box (PIB), for example, is widely used in undergraduate programs to teach the quantum mechanical principles behind the UV--vis spectra of conjugated polyenes and polyynes. In this work, the particle on a ring (POR) and…

We examine students' challenges in determining the number of distinct many-particle stationary states for a system of noninteracting identical particles, focusing on how these insights guided the design, validation, and evaluation of a quantum interactive learning tutorial (QuILT) to aid students' understanding. Specifically, we focus on systems…

It is beneficial for quantum mechanics students to have a unified understanding of eigentheory concepts, so they can recognize the shared structure of mathematized phenomena from the different quantum mechanical systems of spin, energy, or position and recognize those as instantiations of the same overarching concept. Quantum mechanics instructors…

Eigenstates of a quantum mechanical system reflect one to one correspondence with energy level. However, in some systems more than one or a group of eigenstates correspond to a single eigenvalue. To introduce more than one eigenstate corresponding to single energy eigenvalue in 1D-harmonic oscillator, we introduce a new perturbation term and find…

The Gaussian gun is an arrangement of magnets and ball bearings (pictured in Fig. 1) such that--when the leftmost ball is released--the rightmost ball is ejected at high speeds. The device has been described in several articles on energy education. The sudden appearance of kinetic energy offers a productive context for considering a range of…

This is a fundamental and pedagogical work in quantum physics/chemistry, where we try to illustrate the Mulliken's question, "What are the electrons really doing in molecules?". And we also briefly review the development of the most popular numerical approaches in computational chemistry. We examine in a novel approach, how we can…

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] The modern physics course is a crucial gateway for physics majors as it provides an introduction to concepts beyond the scope of the K-12 education. This study collected 167 modern physics syllabi from 127 U.S. research-intensive…

We calculate the frequency of matter-wave of electrons orbiting the hydrogen nucleus at the ground state. It is the same as the value of light frequency corresponding to the ground state from the Rydberg's formula. The result will stimulate students' interest to further understand the mechanisms of quantum theory.

In this paper, an educational tool is proposed to show the internal photoelectric effect in a simple and clear way for Undergraduate Physics courses or High Schools. Experimental evidence of the photoelectric effect is particularly important in the didactic experience. This effect is fundamental to introduce students to the world of quantum…