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On the Origin of Conceptual Difficulties of Quantum Mechanics  [PDF]
Volodymyr Krasnoholovets
Physics , 2004,
Abstract: It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical and high energy physics), the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range action, Heisenberg's uncertainty principle, the passage to the so-called operators of physical values, etc. Orthodox quantum mechanics was constructed as a physical theory developed in the phase space of the mentioned notions. That is why the formalism of quantum mechanics is aimed only at detailed calculations of the stationary states of the energy of the quantum system studied and is not able to describe a real path running by the system in the real space; instead, the formalism gives an averaged probabilistic prediction. Thus, if we are able to develop quantum mechanics in the real space, an option to clarify all the difficulties associated with the above notions would appear. Such a theory of quantum mechanics developed in the real space in fact has recently been constructed by the author. The theory started from deeper first principles, namely, from the consideration of the notion of a 4D space-time. So, the notion of fundamental particle, the principles of the motion of a particle and other characteristics have been made clear. The theory, rather a submicroscopic one, is characterized by short-range action that automatically means the introduction of a new kind of carriers, i.e. carriers of the quantum mechanical force. The existence of the carriers called "inertons" (because they carry inert properties of matter) has indeed been verified in a number of experiments.
Design and validation of the Quantum Mechanics Conceptual Survey
S. B. McKagan,K. K. Perkins,C. E. Wieman
Physical Review Special Topics. Physics Education Research , 2010,
Abstract: The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students’ conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included observations of students, a review of previous literature and textbooks and syllabi, faculty and student interviews, and statistical analysis. We also discuss issues in the development of specific questions, which may be useful both for instructors who wish to use the QMCS in their classes and for researchers who wish to conduct further research of student understanding of quantum mechanics. The QMCS has been most thoroughly tested in, and is most appropriate for assessment of (as a posttest only), sophomore-level modern physics courses. We also describe testing with students in junior quantum courses and graduate quantum courses, from which we conclude that the QMCS may be appropriate for assessing junior quantum courses, but is not appropriate for assessing graduate courses. One surprising result of our faculty interviews is a lack of faculty consensus on what topics should be taught in modern physics, which has made designing a test that is valued by a majority of physics faculty more difficult than expected.
The Design and Validation of the Quantum Mechanics Conceptual Survey  [PDF]
S. B. McKagan,K. K. Perkins,C. E. Wieman
Physics , 2010, DOI: 10.1103/PhysRevSTPER.6.020121
Abstract: The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper we describe the design and validation of the survey, a process that included observations of students, a review of previous literature and textbooks and syllabi, faculty and student interviews, and statistical analysis. We also discuss issues in the development of specific questions, which may be useful both for instructors who wish to use the QMCS in their classes and for researchers who wish to conduct further research of student understanding of quantum mechanics. The QMCS has been most thoroughly tested in, and is most appropriate for assessment of (as a posttest only), sophomore-level modern physics courses. We also describe testing with students in junior quantum courses and graduate quantum courses, from which we conclude that the QMCS may be appropriate for assessing junior quantum courses, but is not appropriate for assessing graduate courses. One surprising result of our faculty interviews is a lack of faculty consensus on what topics should be taught in modern physics, which has made designing a test that is valued by a majority of physics faculty more difficult than expected.
Can Quantum Mechanics be Cleared from Conceptual Difficulties?  [PDF]
Volodymyr Krasnoholovets
Physics , 2002,
Abstract: The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range action, Heisenberg's uncertainty principle, etc. The probabilistic formalism is developed in the phase space, but not in the real one. Elimination of the difficulties is likely if we are able to develop quantum mechanics in the real space. Such a theory in fact can be constructed, however, it should proceed from deepest first principles starting from the notion of a 4D space-time, the notion of a massive particle in the space, the principles of the motion of a particle, etc. The theory should be characterized by short-range action that automatically means the introduction of a quantum mechanical force. It is shown that the aforementioned force makes it evident and, moreover, is able to appear on the macroscopic scale. A simple experiment, the express test, which in fact proves the macroscopic manifestation of quantum mechanical force, is proposed for the demonstration in the quantum curriculum.
Teaching the foundations of quantum mechanics in secondary school: a proposed conceptual structure  [PDF]
Maria de los Angeles Fanaro,Maria Rita Otero,Marcelo Arlego
Investiga??es em Ensino de Ciências , 2009,
Abstract: This paper is part of a doctoral thesis that investigates Basic Quantum Mechanics (QM) teaching in high school. A Conceptual Structure of Reference (CSR) based on the Path Integral Method of Feynman (1965) was rebuilt and a Proposed Conceptual Structure for Teaching (PCST) (Otero, 2006, 2007) the basics of Quantum Mechanics at secondary school was designed, analysed and carried out. This PCST does not follow the historical route and it is complementary to the canonical formalism. The concepts: probability distribution, quantum system, x(t) alternative, amplitude of probability, sum of probability amplitude, action, Planck's constant, and classic-quantum transition were rebuilt with the students. Mathematical formalism was avoided by using simulation software assistance. The Proposed Conceptual Structure for Teaching (PCST) is described and some results from the test carried out by the class group are discussed. This information allows the analysis of the Conceptual Structure Effectively Reconstructed (CSER) to be initiated with the students.
Some conceptual issues involving probability in quantum mechanics  [PDF]
J. Acacio de Barros,Patrick Suppes
Physics , 2000,
Abstract: We discuss some issues about probability in quantum mechanics, with particular emphasis on the GHZ theorem. We propose the usage of nonmonotonic upper probabilities as a tool to derive consistent joint upper probabilities for systems where only contextual hidden variables are possible.
Exploring Student Understanding of Energy through the Quantum Mechanics Conceptual Survey  [PDF]
S. B. McKagan,C. E. Wieman
Physics , 2006,
Abstract: We present a study of student understanding of energy in quantum mechanical tunneling and barrier penetration. This paper will focus on student responses to two questions that were part of a test given in class to two modern physics classes and in individual interviews with 17 students. The test, which we refer to as the Quantum Mechanics Conceptual Survey (QMCS), is being developed to measure student understanding of basic concepts in quantum mechanics. In this paper we explore and clarify the previously reported misconception that reflection from a barrier is due to particles having a range of energies rather than wave properties. We also confirm previous studies reporting the student misconception that energy is lost in tunneling, and report a misconception not previously reported, that potential energy diagrams shown in tunneling problems do not represent the potential energy of the particle itself. The present work is part of a much larger study of student understanding of quantum mechanics.
Conceptual tensions between quantum mechanics and general relativity: Are there experimental consequences?  [PDF]
Raymond Y. Chiao
Physics , 2002,
Abstract: One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash between the spatial nonseparability} of entangled states in QM, and the complete spatial separability of all physical systems in GR, i.e., between the nonlocality implied by the superposition principle, and the locality implied by the equivalence principle. Possible experimental consequences of this conceptual tension will be discussed for macroscopically entangled, coherent quantum fluids, such as superconductors, superfluids, atomic Bose-Einstein condensates, and quantum Hall fluids, interacting with tidal and gravitational radiation fields. A minimal-coupling rule, which arises from the electron spin coupled to curved spacetime, leads to an interaction between electromagnetic (EM) and gravitational (GR) radiation fields mediated by a quantum Hall fluid. This suggests the possibility of a quantum transducer action, in which EM waves are convertible to GR waves, and vice versa.
Conceptual tensions between quantum mechanics and general relativity: Are there experimental consequences?  [PDF]
R. Y. Chiao
Physics , 2003,
Abstract: One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash between the spatial nonseparability of entangled states in QM, and the complete spatial separability of all physical systems in GR, i.e., between the nonlocality implied by the superposition principle, and the locality implied by the equivalence principle. Possible experimental consequences of this conceptual tension will be discussed for macroscopically entangled, coherent quantum fluids, such as superconductors, superfluids, atomic Bose-Einstein condensates, and quantum Hall fluids, interacting with tidal and gravitational radiation fields. A minimal-coupling rule, which arises from the electron spin coupled to curved spacetime, leads to an interaction between electromagnetic (EM) and gravitational (GR) radiation fields mediated by a quantum Hall fluid. This suggests the possibility of a quantum transducer action, in which EM waves are convertible to GR waves, and vice versa.
The Effect of a Thinking Strategy Approach through Visual Representation on Achievement and Conceptual Understanding in Solving Mathematical Word Problems  [cached]
Nasarudin Abdullah,Effandi Zakaria,Lilia Halim
Asian Social Science , 2012, DOI: 10.5539/ass.v8n16p30
Abstract: This quasi-experimental study was designed to determine the effect of a thinking strategy approach through visual representation on the achievement and conceptual understanding in solving mathematical word problems in primary school. The experimental group (n = 96) was exposed to the treatment, while the control group (n = 97) received a conventional approach in teaching and learning mathematical problem solving. To control the variable difference, a pretest was given to both groups before teaching. After 10 weeks of instruction, both groups were given a posttests. Two types of instruments were used to collect the data: the achievement and the conceptual understanding tests. To determine differences between groups, pre and posttests were analyzed using multivariate analysis of variance (MANOVA) followed by univariate analysis of variance (ANOVA). MANOVA results showed a significant difference in overall achievement and understanding of the concept of mathematical word problem solving for the treatment groups as compared to the control group. The ANOVA test of the findings also found that there were significant differences between treatment and control groups. Results showed that students who were exposed to the approach of thinking strategies through visualization representation in mathematical word problem solving outperformed students in conventional classes in achievement and conceptual understanding in mathematical word problem solving. Effect size is high, and therefore the treatment effect is meaningful in practice.
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