The aim of this study was to determine the students' mathematical and conceptual challenges for two important concepts of quantum mechanics and also to investigate how the students make sense of their solutions with the conceptual basis. In this context, open-ended questions were used to determine these difficulties mentioned above. The data collected through the open ended question were analyzed by using the code list and solutions prepared by the researcher. In order to focus on these students' difficulties, semi-structured interviews were done with randomly selected six students from the study group. All of the interviews were video recorded and analyzed according to the prepared coding list. The results of the study show that the students have both conceptual and mathematical difficulties about the commutation relations and expectation value problems which has important place in quantum mechanics.