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We administered written free-response and multiple-choice questions andconducted individual interviews to investigate the difficulties thatupper-level undergraduate and graduate students have with quantum states whiletranslating state vectors in Dirac notation to wave functions in position andmomentum representations. We find that students share common difficulties withtranslating a state vector written in Dirac notation to the wave function inposition or momentum representation.

Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations