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Mar 2008

Volume 76, Issue 3, pp. 197-287

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Resource Letter DEAU-1: Dark energy and the accelerating universe

Eric V. Linder

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 197 | Cited 8 times

Online Publication Date: Feb 2008

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This Resource Letter provides a guide to the literature on dark energy and the accelerating universe. It is intended to be of use to researchers, teachers, and students at several levels. Journal articles, books, and websites are cited for the following topics: Einstein’s cosmological constant, quintessence or dynamical scalar fields, modified cosmic gravity, relations to high-energy physics, cosmological probes and observations, terrestrial probes, calculational tools and parameter estimation, teaching strategies and educational resources, and the fate of the universe.
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01.30.Rr Surveys and tutorial papers; resource letters

Cue and ball deflection (or “squirt”) in billiards

Rod Cross

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 205 | Cited 1 time

Online Publication Date: Feb 2008

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A billiard ball struck by a cue travels in the same direction as the cue unless the ball is struck toward one side in order to impart sidespin. In that case the ball deflects or “squirts” away from the line of approach of the cue, typically by a few degrees. Measurements and calculations are presented showing how a cue tip slides across the ball if it is unchalked, resulting in a large squirt angle, and how it grips the ball when it is chalked, resulting in a smaller squirt angle.
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01.55.+b General physics

A chaotic lock-in amplifier

Brian K. Spears and Nicholas B. Tufillaro

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 213 | Cited 2 times

Online Publication Date: Feb 2008

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We describe a method for lock-in amplification that uses a chaotic reference signal and a synchronized receiver. This technique is compared with conventional lock-in methods using a periodic reference signal. The apparatus can be constructed in an undergraduate electronics lab using a light emitting diode for the transmitter and a photodiode for the receiver, and allows students to explore a novel measurement technique based on chaotic dynamics.
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05.45.-a Nonlinear dynamics and chaos
07.00.00 Instruments, apparatus, and components common to several branches of physics and astronomy

How batteries discharge: A simple model

W. M. Saslow

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 218 | Cited 1 time

Online Publication Date: Feb 2008

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A typical battery is a set of nominally identical voltaic cells in series and/or parallel. We consider the discharge of a single voltaic cell. As the cell discharges due to current-carrying chemical reactions, the densities of the chemical components decrease, which leads to an increase in the internal resistance of the voltaic cell and, upon discharge, a decrease in its terminal voltage and current. A simple model yields behavior similar to what is observed, although accurate battery models are more complex.
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84.30.-r Electronic circuits

A new method to demonstrate frustrated total internal reflection in the visible band

Yizhuang You, Xiaohan Wang, Sihui Wang, Yonghua Pan, and Jin Zhou

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 224 | Cited 2 times

Online Publication Date: Feb 2008

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We describe a new method to demonstrate frustrated total internal reflection in the visible band using the 100 nm thick air film near the center of Newton’s rings. Experimental measurements of the light intensity distribution validate the theoretical predictions.
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42.00.00 Optics

Wavefront sensor with Fresnel zone plates for use in an undergraduate laboratory

Piotr Migdał, Piotr Fita, Czesław Radzewicz, and Łukasz Mazurek

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 229 | Cited 1 time

Online Publication Date: Feb 2008

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We propose a modification of the Shack–Hartmann wavefront sensor in which the lens array is made of Fresnel zone plates. The modification allows students to construct the sensor in an undergraduate laboratory at little cost. In spite of its simplicity the sensor has a sensitivity of λ∕50 in relative measurements, which is sufficient to measure a wavefront of a laser beam distorted by various optical elements as well as by a turbulent airflow. Such an experiment is an excellent supplement to a course in optics, gives students a deeper understanding of the wavefront concept, and demonstrates the wavefront measurement technique widely used in physics, astronomy, and medicine.
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42.00.00 Optics

Coherent states for the bouncing pendulum and the paddle ball

Mark Andrews

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 236

Online Publication Date: Feb 2008

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The coherent states of the simple harmonic oscillator with an impenetrable barrier at its center are studied. This half oscillator is the equivalent of a pendulum that bounces elastically off a vertical wall directly below the point of suspension with the angle of swing sufficiently small. The system can also be considered as a paddle ball, where the paddle is fixed and the ball is constrained by a spring attached to the paddle. The coherent states are almost the same as the familiar Gaussian coherent states of the full oscillator, except when they overlap the barrier. The solutions can be easily extended to two and three dimensions and gravity can be included if the impenetrable barrier is vertical. To better understand the form of the expectation values of the position and momentum, we investigate some general aspects of the effect of impenetrable barriers on the dynamics of wavepackets.
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03.65.-w Quantum mechanics

Investigation of exciton ground state in quantum dots via Hamiltonian diagonalization method

Zachary M. Schultz and John M. Essick

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 241 | Cited 1 time

Online Publication Date: Feb 2008

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We analyze the electron-hole (exciton) ground state associated with the first peak in the optical absorption spectra of semiconductor quantum dots. We assume the effective mass approximation and a dot radius R on the order of the exciton Bohr radius aB. A Hamiltonian diagonalization method which accounts for the exciton’s kinetic, direct Coulomb, and surface polarization energies is used. We obtain a representation of the exciton ground-state wavefunction and a value for its energy using a basis set consisting of only three composite infinite spherical well wavefunctions. We discuss the precision obtained by this basis set by comparing with results from a much more extended basis set. Our results are used to predict the radius-dependent energy of the first peak in visible-light absorption spectra for CdSe quantum dots. Our analysis accurately describes the experimental data for dots with radii in the range aB<R<2aB. We discuss why our model breaks down for smaller radii.
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78.00.00 Optical properties, condensed-matter spectroscopy and other interactions of radiation and particles with condensed matter

Perturbative and nonperturbative studies with the delta function potential

Nabakumar Bera, Kamal Bhattacharyya, and Jayanta K. Bhattacharjee

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 250 | Cited 4 times

Online Publication Date: Feb 2008

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We show that the δ-function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential, if coupled with a δ function potential, remains exactly soluble. We use the strength of the δ function as an expansion parameter and express the second-order energy shift as an infinite sum in perturbation theory. The analytical solution is used to determine the second-order energy shift and hence the sum of an infinite series. By an appropriate choice of the unperturbed system, we can show the importance of the continuum in the energy shift of bound states.
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03.65.-w Quantum mechanics

The Berry phase: A simple derivation and relation to the electric dipole moment experiments with ultracold neutrons

V. K. Ignatovich

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 258

Online Publication Date: Feb 2008

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I derive the effective phase of the spin precession for a neutral particle with spin 1∕2 moving in a superposition of constant and radio frequency fields. The fields are perpendicular to each other at all times, and the radio frequency field is slowly rotating with angular speed ω. The derivation is accomplished with the help of the exact solution of the Schrödinger equation. I show that the geometrical (or Berry) phase is the linear term in the power series expansion of the effective phase in terms of ω. I also discuss the role of the Berry phase in the experimental search for an electric dipole moment of the neutron with ultracold neutrons.
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03.65.-w Quantum mechanics

Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations

Robert J. Nemiroff and Bijunath Patla

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 265 | Cited 1 time

Online Publication Date: Feb 2008

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The general relativistic cosmological Friedmann equations, which describe how the scale factor of the universe evolves, are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations when dominated by a single, isotropic, stable, static, perfect-fluid energy form is discussed for different values of the gravitational pressure to density ratio w. These energy forms include phantom energy (w<−1), cosmological constant (w=−1), domain walls (w=−2∕3), cosmic strings (w=−1∕3), normal matter (w=0), radiation and relativistic matter (w=1∕3), and a previously little-discussed form of energy called “ultralight” (w>1∕3). A brief history and possible futures of Friedmann universes dominated by a single energy form are discussed.
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04.00.00 General relativity and gravitation
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Student understanding of quantum mechanics at the beginning of graduate instruction

Chandralekha Singh

American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 277 | Cited 8 times

Online Publication Date: Feb 2008

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A survey was developed to probe student understanding of quantum mechanics at the beginning of graduate instruction. The survey was administered to 202 physics graduate students enrolled in first-year quantum mechanics courses from seven universities at the beginning of the first semester. We also conducted one-on-one interviews with fifteen graduate or advanced undergraduate students who had just completed a course in which all the content on the survey was covered. Although students from some universities performed better on average than others, we found that students share universal difficulties understanding the concepts of quantum mechanics. The difficulties were often due to overgeneralizations of concepts learned in one context to other contexts where they are not directly applicable. Difficulties in distinguishing between closely related concepts and making sense of the formalism of quantum mechanics were common. The results of this study can sensitize instructors of first-year graduate quantum physics to some of the difficulties students are likely to face.
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01.40.Fk Research in physics education
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