  Identifying and understanding student difficulties with physics content in a
wide variety of topical areas is an active research area within the PER
community. In many cases, physics topics appear multiple times in different
contexts across the undergraduate physics curriculum. As these common topics
reappear, student difficulties can perpetuate from one context to the next, or
new difficulties can emerge as students encounter new physical contexts. One
example of such a topic is boundary conditions. It is broadly considered to be
an important topic that advanced physics undergraduates are expected to
understand and apply in multiple topical areas including classical mechanics,
quantum mechanics, and throughout electricity and magnetism (EM). We report
findings from an investigation of student difficulties using boundary
conditions focusing on the context of electrodynamics. Our data sources include
student responses to traditional exam questions, conceptual survey questions,
and think aloud interviews. The analysis was guided by an analytical framework
that characterizes how students activate, construct, execute, and reflect on
boundary conditions. Common observed student difficulties include: activating
boundary conditions in appropriate contexts; constructing a complex expression
for the E&M waves; mathematically simplifying and manipulating complex
exponential and, checking if the reflection and transmission coefficient are
physical. We also present potential pedagogical implications based on our
observations.
