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Quantum mechanics is a subject rife with student conceptual difficulties. In order to study and devise better strategies for helping students overcome them, we need ways of assessing on a broad level how students are thinking. This is possible with the use of standardized, research-validated assessments like the Quantum Mechanics Concept Assessment (QMCA). These assessments are useful, but they lack rigorous population independence, and the question ordering cannot be rearranged without throwing into question the validity of the results. One way to overcome these two issues is to design the exam to be compatible with Rasch measurement theory which calibrates individual items and is capable of assessing item difficulty and person ability independently. In this paper, we present a Rasch analysis of the QMCA and discuss estimated item difficulties and person abilities, item and person fit to the Rasch model, and unidimensionality of the instrument. This work will lay the foundation for more robust and potentially generalizable assessments in the future.