Mathematical descriptions are the focus of quantum physics education research, as quantum physics is inherently described by its mathematical structures. However, there is a lack of research regarding the role of mathematical descriptions for understanding fundamental principles of quantum physics in teacher preparation and training. In order to investigate how preservice teachers and in-service teachers assess and understand the mathematical formalism in quantum physics, an explorative interview study was conducted. Therefore, we developed a teaching-learning sequence employing a reduced Dirac formalism in the context of single-photon polarization serving as an exemplary two-state system. In that respect, the focus was on two mathematical representations. The ket notation was used as an algebraic representation in connection with the Bloch sphere as a graphical representation of quantum states. On that basis, semistructured and material-based interviews with N=15 preservice teachers and N=15 in-service teachers were conducted. The data suggest that the reduced Dirac formalism is well understood and accepted by both preservice teachers and in-service teachers. However, some in-service teachers raise critical concerns about the abstract nature of the mathematical formalism, pointing to a perceived lack of experimental or phenomenological connection. The ket notation is valued not only for its communicative clarity and its role as a language but also for its structural role. By comparison, the Bloch sphere is met with more cautious acceptance—yet its use in visualizing experiments and measurement processes is positively assessed.