  Development of conceptual multiple-choice tests related to a particular
physics topic is important for designing research-based learning tools to
reduce the difficulties. We explore the difficulties that the advanced
undergraduate and graduate students have with non-relativistic quantum
mechanics of one particle in one spatial dimension. We developed a
research-based conceptual multiple-choice survey that targets these issues to
obtain information about the common difficulties and administered it to more
than a hundred students from seven different institutions. The issues targeted
in the survey include the set of possible wavefunctions, bound and scattering
states, quantum measurement, expectation values, the role of the Hamiltonian,
time-dependence of wavefunction and time-dependence of expectation value. We
find that the advanced undergraduate and graduate students have many common
difficulties with these concepts and that research-based tutorials and
peer-instruction tools can significantly reduce these difficulties. The survey
can be administered to assess the effectiveness of various intructional
strategies.
