Collaborative learning with peers can lead to students learning from each other and solving physics problems correctly not only in situations in which one student knows how to solve the problems but also when none of the students can solve the problems alone. In the latter situation, students are co-constructing knowledge that helps them solve the problems, while in the former, one student helps the other construct knowledge. In this study, we investigated student learning measured by student performance on a validated quantum mechanics survey and frequencies of construction and co-construction of knowledge when students first worked individually after lecture-based instruction in relevant concepts and then worked with peers during class without receiving any feedback from the course instructor. We find that construction of knowledge consistently occurred at a high rate during peer collaboration. However, rates of co-construction were more varied. High rates of co-construction were generally achieved when approximately half of the students knew the correct answers initially.  We also conducted an analysis of some of the survey questions with high rates of co-construction to gain insight into what students converged on after peer interaction and what types of difficulties were reduced. Our findings can be valuable for physics instructors who want to provide in-class and out-of-class opportunities for peer collaboration, e.g., in their quantum mechanics courses.