The Dirac (Bracket) Notation in the Undergraduate Physical Chemistry Curriculum: A Pictorial Introduction

The Dirac (bracket) notation is ubiquitous in the chemical literature, but it is rarely introduced in the undergraduate chemistry curriculum. In this article we present a pictorial approach to the bracket notation that we have successfully used for the past three years in a junior-senior-level physical chemistry course. We have found that it requires roughly 75 minutes to introduce this topic, and, upon integration into subsequent discussions, it prepares our undergraduate students to routinely use this powerful tool in the study of chemical bonding and spectroscopy. We believe that this approach, when introduced after the traditional integral treatment, enhances student learning of the abstract subject of quantum mechanics.