A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, …
A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.
Students practice human-centered design by imagining, designing and prototyping a product to …
Students practice human-centered design by imagining, designing and prototyping a product to improve classroom accessibility for the visually impaired. To begin, they wear low-vision simulation goggles (or blindfolds) and walk with canes to navigate through a classroom in order to experience what it feels like to be visually impaired. Student teams follow the steps of the engineering design process to formulate their ideas, draw them by hand and using free, online Tinkercad software, and then 3D-print (or construct with foam core board and hot glue) a 1:20-scale model of the classroom that includes the product idea and selected furniture items. Teams use a morphological chart and an evaluation matrix to quantitatively compare and evaluate possible design solutions, narrowing their ideas into one final solution to pursue. To conclude, teams make posters that summarize their projects.
Students solidify their understanding of the terms "circumference" and "rotation" through the …
Students solidify their understanding of the terms "circumference" and "rotation" through the use of LEGO MINDSTORMS(TM) NXT robotics components. They measure the circumference of robot wheels to determine how far the robot can travel during one rotation of an NXT motor. They sharpen their metric system measurement skills by precisely recording the length of a wheel's circumference in centimeters, as well as fractions of centimeters. Through this activity, students practice brainstorming ways to solve a problem when presented with a given scenario, improve their ability to measure and record lengths to different degrees of precision, and become familiar with common geometric terms (such as perimeter and rotation).
Add different salts to water, then watch them dissolve and achieve a …
Add different salts to water, then watch them dissolve and achieve a dynamic equilibrium with solid precipitate. Compare the number of ions in solution for highly soluble NaCl to other slightly soluble salts. Relate the charges on ions to the number of ions in the formula of a salt. Calculate Ksp values.
The earliest explorers did not have computers or satellites to help them …
The earliest explorers did not have computers or satellites to help them know their exact location. The most accurate tool developed was the sextant to determine latitude and longitude. In this activity, the sextant is introduced and discussed with the class. Students will learn how a sextant can be a reliable tool that is still being used by today's navigators and how computers can help assure accuracy when measuring angles. Also, this activity will show how computers can be used to understand equations even when knowing how to do the math is unknown.
Introduces students to basic properties of structural materials and behavior of simple …
Introduces students to basic properties of structural materials and behavior of simple structural elements and systems through a series of experiments. Students learn experimental technique, data collection, reduction and analysis, and presentation of results.
Student pairs design, build and test model vehicles capable of rolling down …
Student pairs design, build and test model vehicles capable of rolling down a ramp and then coasting freely as far as possible. The challenge is to make the vehicles entirely out of dry pasta using only adhesive (such as hot glue) to hold the components together. Creativity is encouraged and different types of pasta are provided to support different functions such as round pasta for wheels and sheet pasta for the chassis. Students become familiar with the concepts of gravitational potential energy, kinetic energy and rolling resistance. Teams follow the steps of the engineering design process as they design, test and redesign their small-sized vehicles, working within the project's material constraints. The winner of the competitive final event is the pasta car that travels the longest distance beyond the bottom of the ramp.
Students are introduced to the technology of flexible circuits, some applications and …
Students are introduced to the technology of flexible circuits, some applications and the photolithography fabrication process. They are challenged to determine if the fabrication process results in a change in the circuit dimensions since, as circuits get smaller and smaller (nano-circuits), this could become very problematic. The lesson prepares students to conduct the associated activity in which they perform statistical analysis (using Excel® and GeoGebra) to determine if the circuit dimension sizes before and after fabrication are in fact statistically different. A PowerPoint® presentation and post-quiz are provided. This lesson and its associated activity are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.
Students learn that math is important in navigation and engineering. They learn …
Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts â basic geometry and trigonometry â that have been used for thousands of years.
Students strengthen their communicate skills about measurements by learning the meaning of …
Students strengthen their communicate skills about measurements by learning the meaning of base units and derived units, including speed one of the most common derived units (distance/time). Working in groups, students measure the time for LEGO MINDSTORMS(TM) NXT robots to move a certain distance. The robots are started and stopped via touch sensors and programmed to display the distance traveled. Using their collected data, students complete a worksheet to calculate the robots' (mean/average) speeds at given motor powers.
Students learn about and use a right triangle to determine the width …
Students learn about and use a right triangle to determine the width of a "pretend" river. Working in teams, they estimate of the width of the river, measure it and compare their results with classmates.
In this lesson, students will identify common types of measurements made in …
In this lesson, students will identify common types of measurements made in the lab and the tools used to make those measurements as well as perform measurements in the lab implementing proper use of the metric system and significant figures.
In this less, students will list three (3) common measurement systems used …
In this less, students will list three (3) common measurement systems used in high schools as well as common unit conversion equivalencies and be able to use dimensional analysis to convert between units.
The purpose of this textbook is to help learners develop best practices …
The purpose of this textbook is to help learners develop best practices in vital sign measurement. Using a multi-media approach, it will provide opportunities to read about, observe, practice, and test vital sign measurement.
This review is on the first segment of the Grade 5 curriculum …
This review is on the first segment of the Grade 5 curriculum of "The Inquiry Project: Seeing the World Through the Scientists' Eyes." Water, A Liquid is a series of 5 investigations about water. Students use readily available materials such as water, sand and gravel to deepen their understanding of weight. Having a conceptual understanding of weight is important because students will use it when they begin exploring matter that is too small to be seen. The students are introduced to the study of matter by looking at images of ships sitting in a dry seabed in the Aral Sea. This introductory investigation will hook students because it is posed as a mystery and has a real life connection. Within this series of 5 investigations students will: -practice measurement using standard units -collect and record data -read a letter from an engineer -compare the weight of sand and water -use a digital scale -learn vocabulary -review volume, estimation -engage in discourse -reflect on the weight of small bits of matter -summarize evidence -collaborate -develop strategies -observe -transform (by crushing). The Inquiry Project is a quality curriculum developed pre-NGSS but closely aligned with The Framework of K-12 Science Education. This curriculum "links the three dimensions together" through the qualitative and quantitative measurement of water and sand using standard units and student observations. Each lesson is "designed to link with the previous lesson" as students build toward the capacity to be able to "make observations and measurements to identify materials based on their properties" in the context of the dry sea phenomena.
Students learn the history of the waterwheel and common uses for water …
Students learn the history of the waterwheel and common uses for water turbines today. They explore kinetic energy by creating their own experimental waterwheel from a two-liter plastic bottle. They investigate the transformations of energy involved in turning the blades of a hydro-turbine into work, and experiment with how weight affects the rotational rate of the waterwheel. Students also discuss and explore the characteristics of hydroelectric plants.
Students are introduced to the nano-size length scale as they make measurements …
Students are introduced to the nano-size length scale as they make measurements and calculate unit conversions. They measure common objects and convert their units to nanometers, giving them a simple reference frame for understanding the very small size of nanometers. Then, they compare provided length data from objects too small to measure, such as a human hair and a flea, giving them a comparative insight to the nanotechnology scale. Using familiar and common objects for comparison helps students understand more complex scientific concepts.
Students learn about trigonometry, geometry and measurements while participating in a hands-on …
Students learn about trigonometry, geometry and measurements while participating in a hands-on interaction with LEGO® MINDSTORMS® NXT technology. First they review fundamental geometrical and trigonometric concepts. Then, they estimate the height of various objects by using simple trigonometry. Students measure the height of the objects using the LEGO robot kit, giving them an opportunity to see how sensors and technology can be used to measure things on a larger scale. Students discover that they can use this method to estimate the height of buildings, trees or other tall objects. Finally, students synthesize their knowledge by applying it to solve similar problems. By activity end, students have a better grasp of trigonometry and its everyday applications.
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