Implementing New Educational Platforms in the Classroom: An Interactive Approach to the Particle in a Box Problem

Abstract

The ready availability of interactive platforms has produced a new generation of students able to utilize computer-based learning tools with ease and comfort. The potential to better “explore by yourself” the lecture material permits students to have an enhanced learning experience and stimulates them to tinker with equation parameters generating insightful figures or animations. Used in the classroom, it emboldens students to have a deeper comprehension of complex derivations or mathematical expressions. We illustrate the power of interactive learning platforms by presenting educational Jupyter notebooks for the study of a fundamental problem in quantum chemistry: the motion of a particle in 1D and 2D space. Although simple, this model offers the possibility to explore several important quantum chemistry concepts such as Heisenberg’s uncertainty principle, confinement leading to quantization, tunneling effect, and even bonding and antibonding properties. We present four Jupyter notebooks that gradually walk the student from the properties of a free particle to the properties of a particle in a double potential well. Our experience gained from the implementation of the material in the undergraduate and graduate curriculum is discussed, including student feedback and examples of complementary homework to be used in the classroom.