Abstract
Students in upper division quantum mechanics encounter many difficulties understanding when to and then applying separation of variables technique to solve problems involving partial differential equations.
Highlights
Given the previous work that has been done [33] and our focus on student problem-solving of quantum mechanics, we are interested in three research questions: (1) To what extent can students use partial differential equations (PDEs) tools in the context of quantum physics? That is, when solving a Schrödinger equation in specific situations, how well do students correctly connect the elements of the solving procedure with the physics situations? (2) What are the common difficulties that students encounter when solving a PDE in quantum mechanics? Can we categorize these difficulties? Can we find evidence of possible causes that lead to these difficulties? (3) Compared to previous studies in other contexts, what difficulties are correlated and what difficulties are different?
We find that two kinds of cues in a prompt are likely to activate the mathematical resources associated with these problems
Energy eigenfunction problems are common in quantum mechanics courses, and they are usually solved by analytical methods using differential equations
Summary
There is a growing area of physics education research for the study of students’ difficulties in quantum mechanics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. Students are often asked to use sophisticated mathematical techniques to tackle specific physics problems. There are several investigations on students’ difficulties with solving ordinary differential equations (ODEs) in undergraduate mathematics courses [30,31,32]. We are not aware of any existing research targeting students’ difficulties with differential
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