Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations

TL;DR

This study investigates the common difficulties faced by upper-level undergraduates and graduate students when translating quantum state vectors from Dirac notation to wave functions in position and momentum representations.

Contribution

It provides detailed insights into student misconceptions and challenges in understanding quantum states in different representations, based on assessments and interviews.

Findings

Students struggle with translating Dirac notation to wave functions.

Common misconceptions about quantum state representations.

Identified specific areas where student understanding is limited.

Abstract

We administered written free-response and multiple-choice questions and conducted individual interviews to investigate the difficulties that upper-level undergraduate and graduate students have with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations. We find that students share common difficulties with translating a state vector written in Dirac notation to the wave function in position or momentum representation.