"Pulling out" as a procedural resource when solving partial differential equations

TL;DR

This paper examines how students use a procedural resource called 'pulling out' when solving partial differential equations in quantum mechanics, highlighting its role in their problem-solving process.

Contribution

It identifies and analyzes the procedural resource 'pulling out' as a key element in students' approach to solving PDEs in quantum mechanics.

Findings

Students use 'pulling out' to separate variables in PDEs.

'Pulling out' facilitates students' understanding of wave function separation.

The resource supports sense-making in quantum mechanics problem-solving.

Abstract

We investigate how students solve partial differential equations and partial derivatives in the context of quantum mechanics. We use the resources framework to investigate students' discussion in a group problem-solving environment to investigate the fine-grain elements of their problem solving. We analyze an example of students' use of separation of variables to solve a partial differential equation for a free particle problem. We identify a mathematical action called "pulling out" as a procedural resource to help students with separating the time part from the space part of the wave function in the course of solving the time-dependent Schrodinger equation. We discuss how students use "pulling out" as a procedural step in solving partial differential equations and sense-making.