Understanding Of Quantum Mechanics Research Articles

Interpretation of semiclassical transition moments through wave function expansion of dipole moment functions with applications to the OH stretching spectra of simple acids and alcohols.

Semiclassical description of molecular vibrations has provided us with various computational approximations and enhanced our conceptual understanding of quantum mechanics. In this study, the transition moments of the OH stretching fundamental and overtone intensities (Δv = 1-6) of some alcohols and acids are calculated by three kinds of semiclassical methods, correspondence-principle (CP) approximation, quasiclassical approximation, and uniform WKB approximation, and their respective transition moments are compared to those by the quantum theory. On the basis of the local mode picture, the one-dimensional potential energy curves and the dipole moment functions (DMFs) were obtained by density functional theory calculations and then fitted to Morse functions and sixth-order polynomials, respectively. It was shown that both the transition energies and the absorption intensities derived in the semiclassical methods reproduced their respective quantum values. In particular, the CP approximation reproduces the quantum transition moments if the formula given by Naccache is used for the action integral value. On the basis of these semiclassical results, we present a picture to understand the small variance in the overtone intensities of these acids and alcohols. Another important result is the ratios of semiclassical-to-quantum transition moment are almost independent of the applied molecules even with a great molecular variance of the DMFs, and they depend only on the nature of the semiclassical approximations and the quantum number. The difference between the semiclassical and quantum transition moments was analyzed in terms of a hitherto unrecognized concept that the Fourier expansion of the time dependent DMF in the CP treatment is a kind of the wave function expansion method using trigonometric functions as the quotient functions. For a Morse oscillator, we derive the analytic and approximate expressions of the quotient functions in terms of the bond displace coordinate in both the CP and the quantum mechanical frameworks and discuss the methodological dependence of the calculated transition moments. As a byproduct, we have found a simple derivation of the DMF expression first derived by Timm and Mecke long time ago.

Maximally Nonlocal Theories Cannot Be Maximally Random

Correlations that violate a Bell inequality are said to be nonlocal; i.e., they do not admit a local and deterministic explanation. Great effort has been devoted to study how the amount of nonlocality (as measured by a Bell inequality violation) serves to quantify the amount of randomness present in observed correlations. In this work we reverse this research program and ask what do the randomness certification capabilities of a theory tell us about the nonlocality of that theory. We find that, contrary to initial intuition, maximal randomness certification cannot occur in maximally nonlocal theories. We go on and show that quantum theory, in contrast, permits certification of maximal randomness in all dichotomic scenarios. We hence pose the question of whether quantum theory is optimal for randomness; i.e., is it the most nonlocal theory that allows maximal randomness certification? We answer this question in the negative by identifying a larger-than-quantum set of correlations capable of this feat. Not only are these results relevant to understanding quantum mechanics' fundamental features, but also put fundamental restrictions on device-independent protocols based on the no-signaling principle.

Macroscopic noncontextuality as a principle for almost-quantum correlations

Quantum mechanics allows only certain sets of experimental results (or ``probabilistic models'') for Bell-type quantum nonlocality experiments. A derivation of this set from simple physical or information theoretic principles would represent an important step forward in our understanding of quantum mechanics, and this problem has been intensely investigated in recent years. ``Macroscopic locality,'' which requires the recovery of locality in the limit of large numbers of trials, is one of several principles discussed in the literature that place a bound on the set of quantum probabilistic models. A similar question can also be asked about probabilistic models for the more general class of quantum contextuality experiments. Here, we extend the macroscopic locality principle to this more general setting, using the hypergraph approach of Ac\'{\i}n, Fritz, Leverrier, and Sainz [Comm. Math. Phys. 334(2), 533--628 (2015)], which provides a framework to study both phenomena of nonlocality and contextuality in a unified manner. We find that the set of probabilistic models allowed by our macroscopic noncontextuality principle is equivalent to an important and previously studied set in this formalism, which is slightly larger than the quantum set. In the particular case of Bell scenarios, this set is equivalent to the set of ``almost-quantum'' models, which is of particular interest since the latter was recently shown to satisfy all but one of the principles that have been proposed to bound quantum probabilistic models, without being implied by any of them (or even their conjunction). Our condition is the first characterization of the almost-quantum set from a simple physical principle.

Quantum mechanics concept assessment: Development and validation study

As part of an ongoing investigation of students’ learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum mechanics assessment tool (QMAT) to a multiple-choice (MC) format. Further question refinement, development of effective distractors, adding new questions, and robust statistical analysis has led to a 31-item quantum mechanics concept assessment (QMCA) test. The QMCA is used as post-test only to assess students’ knowledge about five main topics of quantum measurement: the time-independent Schrödinger equation, wave functions and boundary conditions, time evolution, and probability density. During two years of testing and refinement, the QMCA has been given in alpha (N=61) and beta versions (N=263) to students in upper division quantum mechanics courses at 11 different institutions with an average post-test score of 54%. By allowing for comparisons of student learning across different populations and institutions, the QMCA provides instructors and researchers a more standard measure of effectiveness of different curricula or teaching strategies on student conceptual understanding of quantum mechanics. In this paper, we discuss the construction of effective distractors and the use of student interviews and expert feedback to revise and validate both questions and distractors. We include the results of common statistical tests of reliability and validity, which suggest the instrument is presently in a stable, usable, and promising form.3 MoreReceived 22 September 2014DOI:https://doi.org/10.1103/PhysRevSTPER.11.010110This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

A Supplement to the Invariance Principle of the Speed of Light and the Quantum Theory

Richard Feynman once said, “I think it is safe to say that no one understands Quantum Mechanics”. The well-known article on the Einstein-Podolsky-Rosen (EPR) paradox brought forth further doubts on the interpretation of quantum theory. Einstein’s doubt on quantum theory is a doubleedged sword: experimental verification of quantum theory would contradict the hypothesis that speed of light is finite. It has been almost a century since the creation of quantum theory and special relativity, and the relevant doubts brought forward remain unresolved. We posit that the existence of discontinuity points and quantum wormholes would imply superluminal phenomenon or infinite speed of light, which provides for an important supplement to the invariance principle of the speed of light and superluminal phenomena. This can potentially resolve the inconsistency between special relativity and quantum theory.

A unified view on Hardyʼs paradox and the Clauser–Horne–Shimony–Holt inequality

Bellʼs inequality fundamentally changed our understanding of quantum mechanics. Bellʼs insight that non-local correlations between quantum systems cannot be explained classically can be verified experimentally, and has numerous applications in modern quantum information. Today, the Clauser–Horne–Shimony–Holt (CHSH) inequality is probably the most well-known Bell inequality and it has given us a wealth of understanding in what differentiates the classical from the quantum world. Yet, there are certainly other means of quantifying ‘Bell non-locality without inequalities’ such as the famous Hardyʼs paradox. As such, one may wonder whether these are entirely different approaches to non-locality. For this anniversary issue, we unify the perspective of the CHSH inequality and Hardy’s paradox into one family of non-local games which include both as special cases.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

Quantum mechanics: the theoretical minimum

In The Theoretical Minimum, world-class physicist Leonard Susskind provided a brilliant first course in classical mechanics, offering readers not an oversimplified introduction but the real thing - everything you need to start doing physics, and nothing more. Now he returns with the next challenge that every aspiring physics buff must tackle: quantum mechanics. Unlike most popular physics books, Susskind and his co-author Art Friedman teach the maths and equations that are essential to any real understanding of quantum mechanics. Combining crystal-clear explanations, witty and helpful dialogues, and basic exercises, Quantum Mechanics is, to paraphrase Einstein, as simple as possible, but no simpler.

The New Quantum Logic

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.

Quoi de neuf… sur le dépistage organisé du cancer du sein ? Bénéfices soumis à controverse pour taux de couverture encore insuffisant

This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrodinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) maybe a potential source for conflicts; various attitudes that are possible to avoid this problem are discussed in this text. After a brief historical introduction, recalling how the very special status of the state vector has emerged in quantum mechanics, various conceptual difficulties are introduced and discussed. The Einstein Podolsky Rosen (EPR) theorem is presented with the help of a botanical parable, in a way that emphasizes how deeply the EPR reasoning is rooted into what is often called scientific method''. In another section the GHZ argument, the Hardy impossibilities, as well as the BKS theorem are introduced in simple terms.

Geometric Constructions Underlying Relativistic Description of Spin on the Base of Non-Grassmann Vector-Like Variable

Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with complicated structure of constraints. In this work we describe and discuss the spin fiber bundle which appeared in various mechanical models where spin is described by vector-like variable.

Epistemic restrictions in Hilbert space quantum mechanics

A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results in quantum information theory. This analysis provides a quantum mechanical understanding of some recent work that shows that certain kinds of quantum behavior are exhibited by a fully classical model if by hypothesis an observer's knowledge of its state is appropriately limited.

Quantum concepts in physics: an alternative approach to the understanding of quantum mechanics

Written for advanced undergraduates, physicists, and historians and philosophers of physics, this book tells the story of the development of our understanding of quantum phenomena through the extraordinary years of the first three decades of the twentieth century. Rather than following the standard axiomatic approach, this book adopts a historical perspective, explaining clearly and authoritatively how pioneers such as Heisenberg, Schrodinger, Pauli and Dirac developed the fundamentals of quantum mechanics and merged them into a coherent theory, and why the mathematical infrastructure of quantum mechanics has to be as complex as it is. The author creates a compelling narrative, providing a remarkable example of how physics and mathematics work in practice. The book encourages an enhanced appreciation of the interaction between mathematics, theory and experiment, helping the reader gain a deeper understanding of the development and content of quantum mechanics than any other text at this level.

Guest column

The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop tools that address the question: does a quantum version of the PCP theorem hold? The story of this study starts with classical complexity and takes unexpected turns providing fascinating vistas on the foundations of quantum mechanics and multipartite entanglement, topology and the so-called phenomenon of topological order, quantum error correction, information theory, and much more; it raises questions that touch upon some of the most fundamental issues at the heart of our understanding of quantum mechanics. At this point, the jury is still out as to whether or not such a theorem holds. This survey aims to provide a snapshot of the status in this ongoing story, tailored to a general theory-of-CS audience.

Do we really understand quantum mechanics?

Do we really understand quantum mechanics?

At home in the quantum world

One among many misleading quotations about the alleged mysteries of quantum theory is from Feynman (1965): "I think I can safely say that nobody understands quantum mechanics." Today we know that quantum theory describes many aspects of our world in a fully intelligible fashion. Pothos & Busemeyer (P&B) propose ways in which this may include psychology and cognitive science.

Do we really understand quantum mechanics?

Do we really understand quantum mechanics?

Introduction to topological superconductivity and Majorana fermions

This short review paper provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors. We first discuss in some detail the simplest ‘toy model’ in which Majoranas appear, namely a one-dimensional tight-binding representation of a p-wave superconductor, introduced more than 10 years ago by Kitaev. We then give a general introduction to the remarkable properties of Majorana fermions in condensed matter systems, such as their intrinsically non-local nature and exotic exchange statistics, and explain why these quasiparticles are suspected to be especially well suited for low-decoherence quantum information processing. We also discuss the experimentally promising (and perhaps already successfully realized) possibility of creating topological superconductors using semiconductors with strong spin–orbit coupling, proximity-coupled to standard s-wave superconductors and exposed to a magnetic field. The goal is to provide an introduction to the subject for experimentalists or theorists who are new to the field, focusing on the aspects which are most important for understanding the basic physics. The text should be accessible for readers with a basic understanding of quantum mechanics and second quantization, and does not require knowledge of quantum field theory or topological states of matter.

Carlo Cercignani’s interests for the foundations of physics

Carlo Cercignani was known all over the world for his works on the Boltzmann equation and on kinetic theory. There was however another aspect of his scientific life, which is not much known. Namely, his interest for the foundations of physics, in particular for the possibility of understanding quantum mechanics through classical mechanics, which he shared with several people in Milan. A review of such researches is given here, together with some personal recollections of him.

Surveying students’ understanding of quantum mechanics in one spatial dimension

We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 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, and the time-dependence of the wavefunction and expectation values. We find that 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 findings also suggest that graduate quantum mechanics courses may not be effective at helping students to develop a better conceptual understanding of these topics, partly because such courses mainly focus on quantitative assessments.

Analyses of dimensionless science

The intriguing article on dimensional analysis gives rise to a more profound question than the authors explicitly pose: Why should dimensionally nonhomogeneous equations, such as the Manning and Hazen–Williams formulas, be used in hydraulics, or anywhere, when such equations purport to equate apples and oranges?Do our primitive dimensions of mass, space, and time reflect physical reality, or are they biologically adaptive artifacts arising from sensory perceptions? Historically, the sensory perceptions have dominated, beginning with the Greek “elements” of earth, air, fire, and water. That could be making nature seem more complex, and even bizarre, than it truly is, and not just in the case of hydraulics. While some will surely say, “Shut up and calculate,” the question may be worth addressing at a time when many struggle to understand quantum mechanics and the modern cosmological mysteries.© 2012 American Institute of Physics.