  Compared with introductory physics, relatively little is known about the
development of expertise in advanced physics courses, especially in the case of
quantum mechanics. Here, we describe a framework for understanding the patterns
of student reasoning difficulties and how students develop expertise in quantum
mechanics. The framework posits that the challenges many students face in
developing expertise in quantum mechanics are analogous to the challenges
introductory students face in developing expertise in introductory classical
mechanics. This framework incorporates both the diversity in upper-level
students' prior preparation, goals, and motivation in general (i.e., the facts
that even in upper-level courses, students may be inadequately prepared, have
unclear goals, and have insufficient motivation to excel) as well as the
"paradigm shift" from classical mechanics to quantum mechanics. The framework
is based on empirical investigations demonstrating that the patterns of
reasoning, problem-solving, and self-monitoring difficulties in quantum
mechanics bear a striking resemblance to those found in introductory classical
mechanics. Examples from research in quantum mechanics and introductory
classical mechanics are discussed to illustrate how the patterns of
difficulties are analogous as students learn to unpack the respective
principles and grasp the formalism in each knowledge domain during the
development of expertise. Embracing such a framework and contemplating the
parallels between the difficulties in these two knowledge domains can enable
researchers to leverage the extensive literature for introductory physics
education research to guide the design of teaching and learning tools for
helping students develop expertise in quantum mechanics.
