Momentum operators in quantum mechanics

Momentum operators in quantum mechanic

A problem on summation over histories in quantum mechanics

Transition amplitude corresponding to Dirac particle evaluated as sum over histories - quantum mechanic

Path-integrals in dynamics

Path integrals in dynamics - quantum mechanics and classical wave motion in one dimensio

Mental Models Of Groundwater Residence: A Deeper Understanding Of Students’ Preconceptions As A Resource For Teaching And Learning About Groundwater And Aquifers

There is a growing need for public understanding about groundwater resources. Knowing what groundwater and aquifers are is fundamental to understanding more complex issues such as groundwater quality and availability.  However, groundwater and related concepts are among the topics that instructors most struggle to teach.  Although constructivist theories suggest that students’ preconceptions or misconceptions can be used as teaching tools, the question about exactly how remains.  A resource perspective on this question states the first step involves understanding students’ preconceptions. To gain a deeper understanding of college students’ pre-instructional mental models about groundwater residence, 215 students enrolled in introductory-level environmental geoscience courses taught at two large US state universities were surveyed.  An open-ended questionnaire asked participants to draw and label a concept sketch.  Follow-up interviews asked participants to elaborate upon their concept sketches.  Eight categories of mental models emerged from the analysis of the collected data. These results were interpreted through the lens of cognitive schema theory, which generated to four patterns of mental models.  These patterns emphasize key aspects of students’ pre-instructional mental models about groundwater residence.  Instructors can use this information to design instructional activities about groundwater and aquifers using a resource perspective

Decoherence in a double-slit quantum eraser

We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down conversion process, is prepared in a maximally entangled polarization state. A birefringent double-slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled not gate that couples the polarization with the transversal momentum of these photons. The other photon, that acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interferometer is partially unbalanced, it behaves as a controlled source of decoherence for polarization states of down-converted photons. We show the transition from wave-like to particle-like behavior of the signal photons crossing the double-slit as a function of the decoherence parameter, which depends on the length path difference at the interferometer.Comment: Accepted in Physical Review

Cloning and Joint Measurements of Incompatible Components of Spin

A joint measurement of two observables is a {\it simultaneous} measurement of both quantities upon the {\it same} quantum system. When two quantum-mechanical observables do not commute, then a joint measurement of these observables cannot be accomplished by projective measurements alone. In this paper we shall discuss the use of quantum cloning to perform a joint measurement of two components of spin associated with a qubit system. We introduce a cloning scheme which is optimal with respect to this task. This cloning scheme may be thought to work by cloning two components of spin onto its outputs. We compare the proposed cloning machine to existing cloners.Comment: 7 pages, 2 figures, submitted to PR

Control of Ultra-cold Inelastic Collisions by Feshbash Resonances and Quasi-One-Dimensional Confinement

Cold inelastic collisions of atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of the highly vibrationally excited states due to inelastic collisions is suppressed. The relation of our results with those based on the Lieb-Liniger model are addressed.Comment: 5 pages, 1 figur

Drawing As A Method To Facilitate Conceptual Change In Earth Sciences Education

Communicating even fundamental scientific concepts can be challenging. Furthermore, student mental models are often difficult to uncover even by the most talented teacher or researcher. Drawing is a universal process skill widely used by scientists to refine their conceptions about a wide range of topics, communicate ideas, and advance scientific thought in their disciplines. Just as drawing is useful to scientists for refining their conceptions, it has the potential to be useful for revealing misconceptions when teaching from a conceptual change perspective of science students’ mental models. Using a design study methodology and framed within the knowledge integration perspective of conceptual change, this longitudinal study investigates the efficacy of a delimited-sketch activity on the conceptual change of novices’ mental models about groundwater residence. A delimited-sketch activity, the focal case of this study, involves (i) students drawing to expand upon a provided partially-drawn concept sketch and then (ii) collectively debriefing the ideas communicated in the completed student-expanded concept sketches. The activity’s efficacy at facilitating conceptual change is tested with two different sample populations at two different large public universities in the USA. The first population is drawn from an introductory-level college geoscience course designed for non-science majors and the second population is drawn from a similar course designed for science majors. The activity has a large significant impact on moving students away from novice-like toward more expert-like conceptions of groundwater residence. The impact is observed even two months after the activity concludes

The modern tools of quantum mechanics (A tutorial on quantum states, measurements, and operations)

This tutorial is devoted to review the modern tools of quantum mechanics, which are suitable to describe states, measurements, and operations of realistic, not isolated, systems in interaction with their environment, and with any kind of measuring and processing devices. We underline the central role of the Born rule and and illustrate how the notion of density operator naturally emerges, together the concept of purification of a mixed state. In reexamining the postulates of standard quantum measurement theory, we investigate how they may formally generalized, going beyond the description in terms of selfadjoint operators and projective measurements, and how this leads to the introduction of generalized measurements, probability operator-valued measures (POVM) and detection operators. We then state and prove the Naimark theorem, which elucidates the connections between generalized and standard measurements and illustrates how a generalized measurement may be physically implemented. The "impossibility" of a joint measurement of two non commuting observables is revisited and its canonical implementations as a generalized measurement is described in some details. Finally, we address the basic properties, usually captured by the request of unitarity, that a map transforming quantum states into quantum states should satisfy to be physically admissible, and introduce the notion of complete positivity (CP). We then state and prove the Stinespring/Kraus-Choi-Sudarshan dilation theorem and elucidate the connections between the CP-maps description of quantum operations, together with their operator-sum representation, and the customary unitary description of quantum evolution. We also address transposition as an example of positive map which is not completely positive, and provide some examples of generalized measurements and quantum operations.Comment: Tutorial. 26 pages, 1 figure. Published in a special issue of EPJ - ST devoted to the memory of Federico Casagrand

Extending Bauer's corollary to fractional derivatives

We comment on the method of Dreisigmeyer and Young [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems with fractional derivatives. It was previously hoped that using fractional derivatives in an action would allow us to derive a single retarded equation of motion using a variational principle. It is proven that, under certain reasonable assumptions, the method of Dreisigmeyer and Young fails.Comment: Accepted Journal of Physics A at www.iop.org/EJ/journal/JPhys