Physical Sciences and Mathematics Commons^™

Interaction Of Multilevel Atoms With Classical Time-Dependent Fields, Gordon W. F. Drake, R. B. Grimley

Physics Publications

A wide class of problems is considered involving the interaction of multilevel atoms with classical time-dependent fields switched on at a definite time. It is shown that the exact time-dependent Green's function can be written as the particular solution to an inhomogeneous differential equation involving derivatives with respect to the external field variables. Asymptotic expansions are discussed and analytic solutions found for several cases. The time and frequency distributions of radiation emitted by a field-perturbed atom are calculated by including the radiation field as a first-order perturbation. © 1975 The American Physical Society.

Capacitors

Calculus-Based General Physics

Capacitors are important components of electronic circuits and of electrical machinery and power grids. You can find large oil-insulated capacitors on powerline poles or small ceramic-insulated capacitors in a radio. In each application the capacitor is used to store electrical charge and electrical energy - for example, sometimes for a short time in an alternating-current cycle, sometimes for a long time until the energy is needed, as in a strobe light for a camera. Your body can be a capacitor, storing up enough charge and energy to cause a painful spark when the capacitor discharqes.

Practical capacitors are basically two …

Coulomb's Law And The Electric Field

Calculus-Based General Physics

This module beqins the study of electricity. Not only is it true that we see nature's gigantic electrical show in thunderstorm displays with lightning, but the very functioning of our smallest cells depends on the balance of electrically charged ions, and their movement through cell membranes. On a larger scale than cell membranes, water-purification studies with large membranes show promise of "electrically" removing undesired ions or debris from water. The electronic air cleaner is yet another direct application of the material to come: a 7000-V potential difference between a thin wire and flat collecting plates ionizes the air, and the …

Conservation Of Energy

Calculus-Based General Physics

Imagine a bicycle rider coasting without pedaling along a road that is very smooth but has a lot of small hills. As he coasts up a hill, the force of gravity will, of course, slow him down; but it speeds him up again as he goes down the other side. We say that gravity is a conservative force because it gives back as much kinetic energy (KE) to the cyclist when he returns to a lower level, as it took away when he ascended to the top. We therefore assign a gravitational potential energy (PE) U_g to the cyclist, …

Alternating-Current Circuits

Calculus-Based General Physics

The electric clock on the wall, radio and television, the incredibly rapid handling
of information by computers, and the transmission of signals by our own nerves
are among countless devices and effects that depend on circuits in which currents
or voltages vary with time. Alternatinq-current (ac) circuits, in which charges
oscillate back and forth in a wire in such a way that the average current is
zero,are among the simpler time-varying circuits. In this module you will study
the behavior of simple ac circuits containing resistors, inductors, and capacitors.

Gravitation

Calculus-Based General Physics

The members of the solar system -- the Sun, the Moon, and the planets -- have held a strong fascination for mankind since prehistoric times. The motions of these heavenly bodies were thought to have important specific influences on persons' lives -- a belief that is reflected even today in horoscopes and astrological publications. A revolution in man's thinking that occurred about four hundred years ago established the concept of a solar system with planets orbiting about the Sun and moons orbiting about some of the planets. Copernicus, Kepler, Galileo, and Newton were the four scientific leaders chiefly responsible for …

Interference

Calculus-Based General Physics

You may have observed the sound from your radio fade in and out as you listened to some distant station. Or perhaps you have sat in a "dead" seat in a poorly designed concert hall where, despite the fact that no physical object is between you and the performer, the sound is distorted and weak. Perhaps you have held two fingers close together and looked with one eye through the narrow slit separating the fingers and observed those mysterious black lines in and parallel to the slit. These and many other similar phenomena result from the interference of two or …

Flux And Gauss' Law

Calculus-Based General Physics

Charles Augustine de Coulomb (1736-1806) designed his famous experiment to measure the force relationships between charged bodies: Coulomb's law is the resulting empirical statement. Gauss' law (Karl Friedrich Gauss, 1777-1855), which you will learn in this module, has a more obscure origin. It was originally a mathematical theorem. Scientists in Gauss' nineteenth century were much more inclined than we are today to equate mathematical correctness with physical correctness. When it was realized that Gauss' (mathematical) theorem could be applied to the electric-field concepts of Faraday to produce Gauss' (physical) law, this extension was eagerly accepted. The origins of the law, …

Planar Motion

Calculus-Based General Physics

Enough of this physics where things move along straight lines only! We know that most interesting real-life motions involve curves of many and varied shapes. This module extends your understanding of kinematics from one dimension to two dimensions. To accomplish this, you will combine your knowledge of calculus and vectors with concepts like position, displacement, velocity, speed, and acceleration.

Two important applications that will be utilized many times in later modules are covered here. First is the motion of a particle experiencing constant acceleration, e.g., a baseball in flight. Second is the motion of a particle in a circular path …

Rotational Motion

Calculus-Based General Physics

There is a motion of a system of masses that is as simple as the motion of a point mass on a straight line. It is the rotation of a rigid body about a fixed axis. For example, we live on a rotating earth, use rotating devices such as a potter's wheel or a phonograph turntable, and test our luck with a spinning roulette wheel. All of these are objects whose motion is described by the time dependence of a single variable, the angle of rotation. We shall study the angular equivalent of uniformly accelerated motion for some rotating objects. …

Partial Derivatives

Calculus-Based General Physics

If we have a function of more than one independent variable, then we can define a partial derivative with respect to one of the variables, which is simply the derivative of the function with all the other variables fixed, The notation using ∂, which we will use below, tells you it is a partial derivative, For example, suppose we have the function y that depends on the independent variables x and t:

y = A sin(kx – ωt),

where A, k, and ω are constants, Then, "the partial derivative of y with respect to x" …

Calculus

Calculus-Based General Physics

Differentiation of a function, say f(x), is a mathematical operation which yields a second function called the derivative of f [symbolized by f '(x) or dy/dx]. This procedure is represented in the diagram, which shows

Input Differentiation Operation Output

f(x) → f ' (x) = df/dx

the function f(x) being input to an "analytical machine" that manufactures as output the derivative of f. A detailed mathematical prescription for the differentiation operation is nontrivial. It usually involves a quarter or semester course, which requires time, attention, and effort on the student's part.

Traveling Waves

Calculus-Based General Physics

"For many people -- perhaps for most -- the word "wave" conjures up a picture of an ocean, with the rollers sweeping onto the beach from the open sea. If you have stood and watched this phenomenon, you may have felt that for all its grandeur it contains an element of anticlimax. You see the crests racing in, you get a sense of the massive assault by the water on the land -- and indeed the waves can do great damage, which means that they are carriers of energy -- but yet when it is all over, when the wave …

Fluid Mechanics In The Elementary Laboratory, James C. Dennis

Faculty Publications

No abstract provided.

Can Psi Help Him?

Personalized System of Instruction (PSI), or Keller Plan, Materials

PSI (Personalized System of Instruction) can help students learn!

If the lecture-taught course has you meeting the students as adversaries, continually answering redundant questions, haggling over half credit for half correct answers, and generally finding your students being inhibited by the lock-step timing of a lecture course, then PSI is an alternative.

It is also the title of a film, PSI: An Alternative, that imaginatively and graphically outlines an intriguing and dynamic system for learning.

PSI (also known as the Keller Plan) is self-paced, mastery oriented, student tutored for junior college and college level instruction with classes of all sizes …

Personalized System Of Instruction (Psi): An Alternative, James G. Buterbaugh, Robert Fuller

Personalized System of Instruction (PSI), or Keller Plan, Materials

Buterbaugh and Fuller discuss the Personalized System of Instruction--what it is, how it can (or cannot) be evaluated, and some problems which may be encountered with its use. If the lecture-taught course has instructors meeting the students as adversaries, continually answering redundant questions, haggling over half-credit for half-correct answers, and generally finding most students being inhibited by the lock-step timing of a lecture course, then PSI is an alternative. Extensive acceptance and employment of this alternative mode of instruction should cause instructional developers to take another look at the essential features of the system. PSI has been widely employed by …

An Introduction To The Film, Personalized System Of Instruction: An Alternative, Instructional Media Center, University Of Nebraska-­Lincoln

Personalized System of Instruction (PSI), or Keller Plan, Materials

Who should see PSI: An Alternative ?

• Academic classroom instructors from all departments
• Junior college and college administrators
• Teaching method specialists
• Students in schools of education
• Media specialists
• Secondary school educators

You should see PSI: An Alternative.

A digital file of the 14-minute film is attached (below) as a Related File.

Introduction To The Calculus-Based Physics Modules, Robert Fuller

Personalized System of Instruction (PSI), or Keller Plan, Materials

MODULE AUTHORS

OWEN ANDERSON Bucknell University
STEPHEN BAKER Rice University
VAN BLEUMEL Worcester Polytechnic Institute
FERNAND BRUNSCHWIG Empire State College
DAVID JOSEPH University of Nebraska - Lincoln
ROBERT KARPLUS University of California - Berkeley
MICHAEL MOLONEY Rose Hulman Institute of Technology
JACK MUNSEE California State University - Long Beach
GARY NEWBY Boise State University
IVOR NEWSHAM Olivet Nazarene College
WILLIAM SNOW University of Missouri - Rolla
WILLARD SPERRY Central Washington State College
ROBERT SWANSON University of California - San Diego
JAMES TANNER Georgia Institute of Technology
DAVID WINCH Kalamazoo College

These modules were prepared by the module authors at a …

Supersaturated Zincate Solutions, W. Van Doorne, T. P. Dirkse

University Faculty Publications and Creative Works

A study of supersaturated zincate solutions is made using light scattering and nuclear magnetic resonance techniques. The results indicate strongly that the excess zinc is present as a solute species rather than in a colloidal form. The solute species appears to be the same as that in solutions of ZnO in aqueous KOH, viz., Zn(OH)42-. There is no strong evidence to indicate the presence of other solute species.

Electron Impact Autoionization In Heavy Alkali Metals, Kaare J. Nygaard

Physics Faculty Research & Creative Works

Autoionizing levels in cesium, rubidium, and potassium have been studied by electron impact in a crossed-beam apparatus. Comparisons are made with the binary-encounter calculations of Roy and Rai. The effects of autoionization and inner-shell ionization have been overestimated in the theory. © 1975 The American Physical Society.

Measurement Of Growth Rate To Determine Condensation Coefficients For Water Drops Grown On Natural Cloud Nuclei., A. M. Sinnarwalla, Darryl J. Alofs, J. C. Carstens

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Growth Rate Measurements Were Made for Water Drops Grown on Nuclei in Atmospheric Air Samples Taken in Rolla, Missouri. Rolla, Having a Population of 15,000 and Very Little Industry, is Relatively Free of Urban Pollutants. the Measurements Were Made in a Vertical Flow Thermal Diffusion Chamber at Supersaturations of 0. 5 and 1%. the Time to Grow from Near Dry Radius to the Final Radius (6 to 7. 5 Mu M) Was Measured. If One Assumes the Thermal Accomodation Coefficient is Unity, the Measurements Indicate an Average Value of 0. 026 for the Condensation Coefficient. the Temperature Ranged from 22. …

Photoionization Of The 6p32,122 Fine-Structure Levels In Cesium, Kaare J. Nygaard, Robert E. Hebner, James A. Jones, Robert J. Corbin

Physics Faculty Research & Creative Works

The relative photoionization cross sections for cesium atoms selectively excited to the 6P32,122 states have been measured in a triple-crossed-beam experiment. A cesium discharge lamp produced resonant wavelengths of 8521 and 8944 for the excitation process. A Hg-Xe lamp combined with a grating monochromator was used for the actual ionization in the wavelength region from 2500 to 5000. Background counts due to photoionization of ground-state cesium atoms and dimers as well as various surface effects were discriminated against by chopping the excitation light source. The data are compared with results from radiative-recombination measurements in which the fine-structure levels are not …

Strain Effects On The Esr Spectrum From Antimony Donors In Germanium, Edward Boyd Hale, John R. Dennis, Shih Hua Pan

Physics Faculty Research & Creative Works

The electron-spin-resonance spectra from surface-strained (but not externally stressed) antimony-doped germanium are investigated in detail. Experimental data are given for the linewidth, line asymmetry, and line-shape reversal feature as well as for the changes in donor concentration, temperature, and surface conditions. The donors of interest occur in a surface layer several microns thick. A theoretical analysis is based on the Kohn-Luttinger formulation for a shallow donor electron, which is forced by surface strain to predominately occupy a [111] conduction-band valley minimum. A substantial distribution in strain among the donor sites is necessary to account for the line-structure features. These features …

Magnetic Forces

Calculus-Based General Physics

It may surprise you to learn that the conversion of electrical energy to mechanical work in electric motors or stereo loud speakers is seldom done by electrostatic forces (Coulomb's law). Magnetic forces associated with moving charges (currents) are the basis of most electromechanical devices. In analogy with the electrostatic case, we introduce an intermediary called the magnetic field. This module considers the forces on currents or moving charges in a magnetic field; the module Ampere's Law will show how magnetic fields are generated by currents.

Ohm's Law

Calculus-Based General Physics

Recently you have heard many ways of reducing energy consumption in the home. One of the suggested ways is to use 60-W liqht bulbs rather than 100-W bulbs; another is to cut back on the use of electrical appliances. You readily identify these suggestions with decreasing the amount of "electricity" beinq transported through the wires coming into your home.

You were warned quite early in life not to stick a metal knife into the toaster to force out burning bread; you either unplug the toaster or use a utensil with a wooden handle. Why? Because you were warned of the …

Newton's Laws

Calculus-Based General Physics

When a body is at rest, we know from experience that it will remain at rest unless something is done to change that state. A heavy box on the floor will stay in place unless it is pushed or pulled. We walk without fear beside a massive rock on level ground because we know it won't suddenly move and crush us.

Undoubtedly you have leaned against a chair only to have it move and send you scurrying for your balance. Did you then question the relationship of the interaction between you and the chair to the ensuing motion of the …

Reflection And Refraction

Calculus-Based General Physics

Sight is certainly one of our most important senses and depends on the interaction of electromagnetic waves in the visible portion of the spectrum with the eye. The use of materials that reflect light and that refract or "bend" light extends throughout our industrialized society. In this module we deal with light traveling in two dimensions and encounterinq the boundaries between media under those conditions in which the wavelength is small compared with the size of the obstacles or apertures. Under such conditions, since diffraction and interference effects are negligible, the principal phenomena occurring at the interfaces, reflection and refraction, …

Rotational Dynamics

Calculus-Based General Physics

A diver, in making several turns in the air, grabs his knees to achieve a high rate of rotation, and a skater does much the same thing when she goes into a spin with arms and legs extended but brings them in close to her body for the extremely rapid part of this motion. This module considers the physics describing these motions, and those of other rotational systems -- starting or stopping a record turntable (or a washing-machine tub), unwinding of winch cord as a bucket is dropped into a well, etc.

Relativity

Calculus-Based General Physics

Seldom has a development in science captured the attention of the general populace to the extent that Einstein's special theory of relativity did. Once, after giving a public lecture, Einstein was on the way to the railroad depot when he was asked to summarize his theory in one sentence, in a way the general public could understand. His reply: "When does the station get to the train?" Many of the predictions of the theory violate common sense -- lengths change, times change, masses change, depending on who is looking -- but the theory has been proved correct whenever it has …

Second Law And Entropy

Calculus-Based General Physics

Suppose you get into your car and drive to _________.* During this trip, (1) the burning of the gasoline in the engine cylinders converts chemical energy into thermal energy of the gases -- that is, they become very hot; (2) the expansion of these hot gases turns the crankshaft, performing work; and (3) this work, transmitted to the wheels, gives the car kinetic energy -- which must be continually replenished, because of depletion by friction and air resistance. At the end of this trip, ____ gallons of gasoline have been converted into water vapor, carbon dioxide, and sundry less desirable …