|Title||Student Reasoning with Completeness Relations in Quantum Mechanics|
|Year of Publication||2021|
|Authors||Gire, Elizabeth, Grant Sherer, Maggie Greenwood, and Corinne A. Manogue|
|Venue/Conference||Physics Education Research Conference|
|City||Remote via Underline|
Using a completeness (or closure) relation is a neat math trick in quantum theory. Completeness relations capture the fundamental property that a basis set spans a vector space, and conceptually can be thought of as a special form of the identity operator. In quantum mechanics, completeness relations can be used to express a quantum state in a particular basis, change which basis a state is expressed in, as well as mathematically model the effect of a quantum interferometer. We have analyzed students' written responses to homework and final exam questions related to completeness relations from a junior-level, introduction to quantum mechanics course. In this poster, we will present student reasoning and difficulties using completeness relations.