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It is linguistically awkward to speak of the potential energy "inside the barrier" since the potential energy is the barrier, but it is important to be explicit, as many students do not recognize the equivalence of potential energy and barrier.
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It is linguistically awkward to speak of the potential energy "inside the barrier" since the potential energy is the barrier, but it is important to be explicit, as many students do not recognize the equivalence of potential energy and barrier.
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The simulation discussed in the next section uses both labels to help students relate the more correct term to the term that is more commonly used in textbooks.
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The simulation discussed in the next section uses both labels to help students relate the more correct term to the term that is more commonly used in textbooks.
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26
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55849095336
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36
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55849121053
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While the transformed curriculum was designed specifically for engineering majors, it was used in the physics majors' course in the semester following this study. This course was not included in the study due to lack of time. Anecdotal observations suggest that the physics majors tended to pick up on things faster, so that the prevalence of many of the difficulties cited here was somewhat less for them, but the qualitative results of this study were not significantly different for this population.
-
While the transformed curriculum was designed specifically for engineering majors, it was used in the physics majors' course in the semester following this study. This course was not included in the study due to lack of time. Anecdotal observations suggest that the physics majors tended to pick up on things faster, so that the prevalence of many of the difficulties cited here was somewhat less for them, but the qualitative results of this study were not significantly different for this population.
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37
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The Activity-Based Tutorials (Ref.), one of which we adapted for use in our curriculum, also include several exercises for building up the idea of potential-energy graphs through laboratory activities with carts on magnetic tracks. We did not use these activities due to lack of time and lack of a laboratory section in our course and because we were more interested in helping students understand potential-energy diagrams for real quantum systems than for classical systems. However, our research indicates that such an approach could be useful if connections are made between these classical examples and examples of systems where quantum mechanics applies.
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The Activity-Based Tutorials (Ref.), one of which we adapted for use in our curriculum, also include several exercises for building up the idea of potential-energy graphs through laboratory activities with carts on magnetic tracks. We did not use these activities due to lack of time and lack of a laboratory section in our course and because we were more interested in helping students understand potential-energy diagrams for real quantum systems than for classical systems. However, our research indicates that such an approach could be useful if connections are made between these classical examples and examples of systems where quantum mechanics applies.
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