This study presents a review of the current state of research on teaching quantum mechanics in secondary and lower undergraduate education. A conceptual approach to quantum mechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantum mechanics and classical physics, research on misconceptions, testing, and teaching strategies for introductory quantum mechanics is needed. For this review, 74 articles were selected and analyzed for the misconceptions, research tools, teaching strategies, and multimedia applications investigated. Outcomes were categorized according to their contribution to the various subtopics of quantum mechanics. Analysis shows that students have difficulty relating quantum physics to physical reality. It also shows that the teaching of complex quantum behavior, such as time dependence, superposition, and the measurement problem, has barely been investigated for the secondary and lower undergraduate level. At the secondary school level, this article shows a need to investigate student difficulties concerning wave functions and potential wells. Investigation of research tools shows the necessity for the development of assessment tools for secondary and lower undergraduate education, which cover all major topics and are suitable for statistical analysis. Furthermore, this article shows the existence of very diverse ideas concerning teaching strategies for quantum mechanics and a lack of research into which strategies promote understanding. This article underlines the need for more empirical research into student difficulties, teaching strategies, activities, and research tools intended for a conceptual approach for quantum mechanics.

This article describes a Delphi study aiming to investigate which quantum mechanics topics experts consider to be important to teach at the secondary level, and what arguments these experts give. A series of three questionnaires was administered to experts in the fields of quantum physics, mathematics, chemistry and biophysics (n = 17, 12, 11 for the first, second, and third questionnaires, respectively; the number of participants changed due to attrition). Several experts from this group (n = 9) were also interviewed. Results show that there is consensus on the topics considered to be important, i.e. duality, wave functions and atoms. Experts mainly based their topic ranking on relations between concepts, and on what quantum mechanics topics they consider to be fundamental. The topics that were considered less important were often described as too difficult or too complex. ARTICLE HISTORY

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In order to investigate students' misunderstandings of potential wells and tunneling, a conceptual knowledge test was administered to Dutch secondary school students after they were taught about quantum mechanics. A frequency analysis of responses to the multiple choice questions (n ¼ 98) and coding of the responses to the open-ended questions and explanations (n ¼ 13) shows that Dutch secondary school students experience difficulties similar to those reported for undergraduate students. The students' underlying difficulties were analyzed using a typology of learning impediments. Results of this analysis show that students have difficulty connecting knowledge of potential wells and tunneling to their prior knowledge. Students mainly have creative and epistemological learning impediments, which cause eight incorrect synthetic models.

Classical prediction RealityWavelength FIGURE 1 The energy emitted by a black body depending on the wavelength, based on classical mechanics and on measurements.ATOMIC SPECTRA -THE WAVE BEHAVIOUR OF PARTICLES Based on the relation between energy and wavelength, as presented by Planck and Einstein, in 1913 Bohr proposed his atomic model 4 . In this atomic model Bohr stated that there were specific permitted orbits for electrons, which could explain the spectrum of hydrogen. Electrons would jump from one orbit to another, causing light to be emitted, with a wavelength that corresponded to the change in energy. Although Bohr's atomic model corresponded with the experimentally observed spectral lines of hydrogen, it gave no physical explanation for the existence of the specific permitted orbits. De Broglie related these specific permitted orbits and the stable motions of electrons in the atom to wave behaviour 5 , and was the first to assign wave properties to particles in order to explain these orbits 6 . De Broglie's 4 Chapter 1 things beyond expectation, but it remains under discussion wat QM implies for the way we understand what physical reality is. TEACHING QUANTUM MECHANICS'Lately, a lot is going on in physics, and I think there is also a widespread feeling among teachers, that they stand for an evolution.'