We have investigated student difficulties in understanding and interpreting probability and its relevant technical terms as it relates to quantum measurement. These terms include expectation value, probability density, and uncertainty. From this research, it is evident that students have difficulties in understanding these terms and often fail to differentiate among similar but different concepts.
In addition, students' difficulties with the concepts of probability often interfere with their understanding and application of the Uncertainty Principle. For example, many Since the beginning of history, in a world of studies in mathematics education and cognitive uncertainty, man has pursued certainty.
The mission psychology report student difficulties in this topic [6]. Later, with the Recent developments in nanotechnology, development of Newtonian mechanics the photonics, and superconductivity bring to our deterministic worldview remained entrenched. It was everyday life advanced engineering and business only with the advance of thermodynamics that devices that can be explained only through principles Boltzmann introduced the idea of probability into of quantum mechanics.
The framework of quantum physical law. In the same way for most students, a mechanics introduces the ideas of probabilities, wave- quantum mechanics course is the first time a physical particle duality, and non-locality into the foundation of concept has been explained in terms of probability.
It physics. These new ideas are abstract and usually is often difficult for them to replace the basic difficult for introductory college students. For example, Bao mechanics classes, in the study of students' written and Redish suggest that probabilistic interpretations of homework, and in one-on-one interactions, we physical systems are a prerequisite to learning observed that students often have trouble with the quantum physics [2].
For example, in many cases quantum measurement. In addition, measurement, and identical particles. Singh [4] has they had difficulties in constructing a physical constructed a list of student misconceptions in the meaning for quantitative values of these terms. For domain of quantum measurement and time evolution. Heron, L. McCullough, and J. S4: " First, the can have any value. These initial observations motivated us to Students had difficulties with both parts of the systematically investigate students' understanding of solution.
Many students were not able to calculate the probability and related concepts. This specific function in this problem represents the wavefunction situation, when the probability density in position in position space and not in momentum space. In addition to formal methods, such as individual interviews, written questions, and First, this student confuses the Fourier transform of the multiple-choice questionnaires, we have also collected wavefunction with the expectation value of x.
Emma is solving a quantum problem. She is Q2. Choose all that apply. Explain your reasoning. Questions on probability densities, expectation values, and uncertainties in The correct answers to Q2 are choices b , d , and measurement were given to students in all three classes e ; nevertheless, none of the students picked the [9].
Questions Q1 and Q2 are examples of such. Although had also a correct reasoning [See Table 2]. Due to the higher-level content of this that befits an expectation value. This reasoning fails to question [10], we gave this question only to the correctly apply the Uncertainty Principle. Students were also asked to explain their reasoning.
Wigner, Phys. Barut, Phys. Scully and L. Cohen, Found. Kim and W. Zachary, eds. Springer, New York, Greenberger, ed. Marlow, ed. Academic Press, New York, Altes, personal communication Technical Memorandum , Orincon, April Download references. You can also search for this author in PubMed Google Scholar.
Reprints and Permissions. Cohen, L. Rules of probability in quantum mechanics. Found Phys 18, — Download citation. Received : 12 October Issue Date : October Anyone you share the following link with will be able to read this content:.
Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content. Search SpringerLink Search. Abstract We show that the quantum mechanical rules for manipulating probabilities follow naturally from standard probability theory. References 1. Google Scholar 2. Google Scholar 3. Google Scholar 5. Article Google Scholar 6. Google Scholar 7.
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