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PHYSICS 1 Emerson College De Broglie Wavelength Quantum Mechanics Physics Notes

Physics 1

Emerson College

PHYSICS

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Hello I need 8 pages of notes on selected sections of 2 Physics books, these notes are precise, not too good, and for a sophomore in college Level. I will provide the books the sections that you need to write from. I want the notes to be separated into three sections: special relativity, waves, quantum mechanics. The second book is too big to upload here so when you accept I will send it by Google Drive, it’s by the same writer.

PHYSICS 1 Emerson College De Broglie Wavelength Quantum Mechanics Physics Notes
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PHYSICS 1 Emerson College De Broglie Wavelength Quantum Mechanics Physics Notes
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PHYSICS 1 Emerson College De Broglie Wavelength Quantum Mechanics Physics Notes
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Fundamentals of Physics t h e o p e n y a l e c o u r s e s s e r i e s is designed to bring the depth and breadth of a Yale education to a wide variety of readers. Based on Yale’s Open Yale Courses program (http://oyc.yale.edu), these books bring outstanding lectures by Yale faculty to the curious reader, whether student or adult. Covering a wide variety of topics across disciplines in the social sciences, physical sciences, and humanities, Open Yale Courses books offer accessible introductions at affordable prices. The production of Open Yale Courses for the Internet was made possible by a grant from the William and Flora Hewlett Foundation. RECENT TITLES Paul H. Fry, Theory of Literature Christine Hayes, Introduction to the Bible Shelly Kagan, Death Dale B. Martin, New Testament History and Literature Giuseppe Mazzotta, Reading Dante R. Shankar, Fundamentals of Physics Ian Shapiro, The Moral Foundations of Politics Steven B. Smith, Political Philosophy Fundamentals of Physics Mechanics, Relativity, and Thermodynamics r. s h a n k a r New Haven and London Published with assistance from the foundation established in memory of Amasa Stone Mather of the Class of 1907, Yale College. c 2014 by Yale University. Copyright  All rights reserved. This book may not be reproduced, in whole or in part, including illustrations, in any form (beyond that copying permitted by Sections 107 and 108 of the U.S. Copyright Law and except by reviewers for the public press), without written permission from the publishers. Yale University Press books may be purchased in quantity for educational, business, or promotional use. For information, please e-mail sales.press@ yale.edu (U.S. office) or sales@yaleup.co.uk (U.K. office). Set in Minion type by Newgen North America. Printed in the United States of America. ISBN: 978-0-300-19220-9 Library of Congress Control Number: 2013947491 A catalogue record for this book is available from the British Library. This paper meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). 10 9 8 7 6 5 4 3 2 1 To my students for their friendship and inspiration Deep and original, but also humble and generous, the physicist Josiah Willard Gibbs spent much of his life at Yale University. His father was a professor of sacred languages at Yale, and Gibbs received his bachelor’s and doctorate degrees from the university before teaching there until his death in 1903. The sculptor Lee Lawrie created the memorial bronze tablet pictured above, which was installed in Yale’s Sloane Physics Laboratory in 1912. It now resides in the entrance to the J. W. Gibbs Laboratories, Yale University. Contents Preface xiii 1. The Structure of Mechanics 1.1 Introduction and some useful tips 1.2 Kinematics and dynamics 1.3 Average and instantaneous quantities 1.4 Motion at constant acceleration 1.5 Sample problem 1.6 Deriving v2 = v02 + 2a(x − x0 ) using calculus 1 1 2 4 6 10 13 2. Motion in Higher Dimensions 2.1 Review 2.2 Vectors in d = 2 2.3 Unit vectors 2.4 Choice of axes and basis vectors 2.5 Derivatives of the position vector r 2.6 Application to circular motion 2.7 Projectile motion 15 15 16 19 22 26 29 32 3. Newton’s Laws I 3.1 Introduction to Newton’s laws of motion 3.2 Newton’s second law 3.3 Two halves of the second law 3.4 Newton’s third law 3.5 Weight and weightlessness 36 36 38 41 45 49 4. Newton’s Laws II 4.1 A solved example 4.2 Never the whole story 4.3 Motion in d = 2 51 51 54 55 viii Contents 4.4 4.5 4.6 4.7 Friction: static and kinetic Inclined plane Coupled masses Circular motion, loop-the-loop 56 57 61 64 5. Law of Conservation of Energy 5.1 Introduction to energy 5.2 The work-energy theorem and power 5.3 Conservation of energy: K2 + U2 = K1 + U1 5.4 Friction and the work-energy theorem 70 70 71 75 78 6. Conservation of Energy in d = 2 6.1 Calculus review 6.2 Work done in d = 2 6.3 Work done in d = 2 and the dot product 6.4 Conservative and non-conservative forces 6.5 Conservative forces 6.6 Application to gravitational potential energy 82 82 84 88 92 95 98 7. The Kepler Problem 7.1 Kepler’s laws 7.2 The law of universal gravity 7.3 Details of the orbits 7.4 Law of conservation of energy far from the earth 7.5 Choosing the constant in U 101 101 104 108 112 114 8. Multi-particle Dynamics 8.1 The two-body problem 8.2 The center of mass 8.3 Law of conservation of momentum 8.4 Rocket science 8.5 Elastic and inelastic collisions 8.6 Scattering in higher dimensions 118 118 119 128 134 136 140 9. Rotational Dynamics I 9.1 Introduction to rigid bodies 9.2 Angle of rotation, the radian 143 143 145 Contents 9.3 9.4 9.5 9.6 ix Rotation at constant angular acceleration Rotational inertia, momentum, and energy Torque and the work-energy theorem Calculating the moment of inertia 147 148 154 156 10. Rotational Dynamics II 10.1 The parallel axis theorem 10.2 Kinetic energy for a general N-body system 10.3 Simultaneous translations and rotations 10.4 Conservation of energy 10.5 Rotational dynamics using τ = dL dt 10.6 Advanced rotations 10.7 Conservation of angular momentum 10.8 Angular momentum of the figure skater 159 159 163 165 167 168 169 171 172 11. Rotational Dynamics III 11.1 Static equilibrium 11.2 The seesaw 11.3 A hanging sign 11.4 The leaning ladder 11.5 Rigid-body dynamics in 3d 11.6 The gyroscope 175 175 176 178 180 182 191 12. Special Relativity I: The Lorentz Transformation 12.1 Galilean and Newtonian relativity 12.2 Proof of Galilean relativity 12.3 Enter Einstein 12.4 The postulates 12.5 The Lorentz transformation 194 195 196 200 203 204 13. Special Relativity II: Some Consequences 13.1 Summary of the Lorentz transformation 13.2 The velocity transformation law 13.3 Relativity of simultaneity 13.4 Time dilation 13.4.1 Twin paradox 13.4.2 Length contraction 209 209 212 214 216 219 220 x Contents 13.5 More paradoxes 13.5.1 Too big to fall 13.5.2 Muons in flight 222 222 226 14. Special Relativity III: Past, Present, and Future 14.1 Past, present, and future in relativity 14.2 Geometry of spacetime 14.3 Rapidity 14.4 Four-vectors 14.5 Proper time 227 227 232 235 238 239 15. Four-momentum 15.1 Relativistic scattering 15.1.1 Compton effect 15.1.2 Pair production 15.1.3 Photon absorption 241 249 249 251 252 16. Mathematical Methods 16.1 Taylor series of a function 16.2 Examples and issues with the Taylor series 16.3 Taylor series of some popular functions 16.4 Trigonometric and exponential functions 16.5 Properties of complex numbers 16.6 Polar form of complex numbers 255 255 261 263 265 267 272 17. Simple Harmonic Motion 17.1 More examples of oscillations 17.2 Superposition of solutions 17.3 Conditions on solutions to the harmonic oscillator 17.4 Exponential functions as generic solutions 17.5 Damped oscillations: a classification 17.5.1 Over-damped oscillations 17.5.2 Under-damped oscillations 17.5.3 Critically damped oscillations 17.6 Driven oscillator 275 280 283 288 290 291 291 292 294 294 Contents xi 18. Waves I 18.1 The wave equation 18.2 Solutions of the wave equation 18.3 Frequency and period 303 306 310 313 19. Waves II 19.1 Wave energy and power transmitted 19.2 Doppler effect 19.3 Superposition of waves 19.4 Interference: the double-slit experiment 19.5 Standing waves and musical instruments 316 316 320 323 326 330 20. Fluids 20.1 Introduction to fluid dynamics and statics 20.1.1 Density and pressure 20.1.2 Pressure as a function of depth 20.2 The hydraulic press 20.3 Archimedes’ principle 20.4 Bernoulli’s equation 20.4.1 Continuity equation 20.5 Applications of Bernoulli’s equation 335 335 335 336 341 343 346 346 349 21. Heat 21.1 Equilibrium and the zeroth law: temperature 21.2 Calibrating temperature 21.3 Absolute zero and the Kelvin scale 21.4 Heat and specific heat 21.5 Phase change 21.6 Radiation, convection, and conduction 21.7 Heat as molecular kinetic energy 352 352 354 360 361 365 368 371 22. Thermodynamics I 22.1 Recap 22.2 Boltzmann’s constant and Avogadro’s number 22.3 Microscopic definition of absolute temperature 22.4 Statistical properties of matter and radiation 22.5 Thermodynamic processes 375 375 376 379 382 384 xii Contents 22.6 Quasi-static processes 22.7 The first law of thermodynamics 22.8 Specific heats: cv and cp 386 387 391 23. Thermodynamics II 23.1 Cycles and state variables 23.2 Adiabatic processes 23.3 The second law of thermodynamics 23.4 The Carnot engine 23.4.1 Defining T using Carnot engines 394 394 396 399 403 409 24. Entropy and Irreversibility 24.1 Entropy 24.2 The second law: law of increasing entropy 24.3 Statistical mechanics and entropy 24.4 Entropy of an ideal gas: full microscopic analysis 24.5 Maximum entropy principle illustrated 24.6 The Gibbs formalism 24.7 The third law of thermodynamics 411 411 418 423 430 434 437 441 Index 443 Preface Given that the size of textbooks has nearly tripled during my own career, without a corresponding increase in the cranial dimensions of my students, I have always found it necessary, like my colleagues elsewhere, to cull the essentials into a manageable size. I did that in the course Fundamentals of Physics I taught at Yale, and this book preserves that feature. It covers the fundamental ideas of Newtonian mechanics, relativity, fluids, waves, oscillations, and thermodynamics without compromise. It requires only the basic notions of differentiation and integration, which I often review as part of the lectures. It is aimed at college students in physics, chemistry, and engineering as well as advanced high school students and independent self-taught learners at various stages in life, in various careers. The chapters in the book more or less follow my 24 lectures, with a few minor modifications. The style preserves the classroom atmosphere. Often I introduce the questions asked by the students or the answers they give when I believe they will be of value to the reader. The simple figures serve to communicate the point without driving up the price. The equations have been typeset and are a lot easier to read than in the videos. The problem sets and exams, without which one cannot learn or be sure one has learned the physics, may be found along with their solutions at the Yale website, http://oyc.yale.edu/physics, free and open to all. The lectures may also be found at venues such as YouTube, iTunes (https://itunes.apple.com/us/itunes-u/physicsvideo/id341651848?mt=10), and Academic Earth, to name a few. The book, along with the material available at the Yale website, may be used as a stand-alone resource for a course or self-study, though some instructors may prescribe it as a supplement to another one adapted for the class, so as to provide a wider choice of problems or more worked examples. To my online viewers I say, “You have seen the movie; now read the book!” The advantage of having the printed version is that you can read it during take-off and landing. xiii xiv Preface In the lectures I sometimes refer to my Basic Training in Mathematics, published by Springer and intended for anyone who wants to master the undergraduate mathematics needed for the physical sciences. This book owes its existence to many people. It all began when Peter Salovey, now President, then Dean of Yale College, asked me if I minded having cameras in my Physics 200 lectures to make them part of the first batch of Open Yale Courses, funded by the Hewlett Foundation. Since my answer was that I had yet to meet a camera I did not like, the taping began. The key person hereafter was Diana E. E. Kleiner, Dunham Professor, History of Art and Classics, who encouraged and guided me in many ways. She was also the one who persuaded me to write this book. Initially reluctant, I soon found myself thoroughly enjoying proselytizing my favorite subject in this new format. At Yale Universtity Press, Joe Calamia was my friend, philosopher, and guide. Liz Casey did some very skilled editing. Besides correcting errors in style (such as a long sentence that began in first person past tense and ended in third person future tense) and matters of grammar and punctuation (which I sprinkle pretty much randomly), she also made sure my intent was clear in every sentence. Barry Bradlyn and Alexey Shkarin were two graduate students and Qiwei Claire Xue and Dennis Mou were two undergraduates who proofread earlier versions. My family, from my wife, Uma, down to little Stella, have encouraged me in various ways. I take this opportunity to acknowledge my debt to the students at Yale who, over nearly four decades, have been the reason I jump out of bed on two or three days a week. I am grateful for their friendship and curiosity. In recent years, they were often non-majors, willing to be persuaded that physics was a fascinating subject. This I never got tired of doing, thanks to the nature of the subject and the students. chapter 1 The Structure of Mechanics 1.1 Introduction and some useful tips This book is based on the first half of a year-long course that introduces you to all the major ideas in physics, starting from Galileo and Newton, right up to the big revolutions of the twentieth century: relativity and quantum mechanics. The target audience for this course and book is really very broad. In fact, I have always been surprised by the breadth of interests of my students. I don’t know what you are going to do later in life, so I have picked the topics that all of us in physics find fascinating. Some may not be useful, but you just don’t know. Some of you are probably going to be doctors, and you don’t know why I’m going to cover special relativity or quantum mechanics. Well, if you’re a doctor and you have a patient who’s running away from you at the speed of light, you’ll know what to do. Or, if you’re a pediatrician, you will understand why your patient will not sit still: the laws of quantum mechanics don’t allow a very small object to have a definite position and momentum. Whether or not you become a physicist, you should certainly learn about these great strides in the human attempt to understand the physical world. Most textbooks are about 1,200 pages long, but when I learned physics they were around 400 pages long. When I look around, I don’t see any student whose head is three times as big as mine, so I know that you cannot digest everything the books have. I take what I think are the really essential parts and cover them in these lectures. So you need the lectures to find out what’s in the syllabus and what’s not. If you don’t do that, 1 2 The Structure of Mechanics there’s a danger you will learn something you don’t have to, and we don’t want that, right? To learn physics well, you have to do the problems. If you watch me online doing things on the blackboard or working through derivations in the book, it all looks very reasonable. It looks like you can do it yourself and that you understand what is going on, but the only way you’re going to find out is by actually doing problems. A fair number are available, with their solutions, at http://oyc.yale.edu/physics/phys-200. You don’t have to do them by yourself. That’s not how physics is done. I am now writing a paper with two other people. My experimental colleagues write papers with four hundred or even a thousand other people when engaged in the big collider experiments like the ones in Geneva or Fermilab. It’s perfectly okay to be part of a collaboration, but you have to make sure that you’re pulling your weight, that everybody makes contributions to finding the solution and understands it. This calculus-based course assumes you know the rudiments of differential and integral calculus, such as functions, derivatives, derivatives of elementary functions, elementary integrals, changing variables in integrals, and so on. Sometime later, I will deal with functions of more than one variable, which I will briefly introduce to you, because that is not a prerequisite. You have to know your trigonometry, to know what’s a sine and what’s a cosine and some simple identities. You cannot say, “I will look it up.” Your birthday and social security number are things you look up; trigonometric functions and identities are what you know all the time. 1.2 Kinematics and dynamics We are going to be studying Newtonian mechanics. Standing on the shoulders of his predecessors, notably Galileo, Isaac Newton placed us on the road to understanding all the mechanical phenomena for centuries until the laws of electromagnetism were discovered, culminating in Maxwell’s equations. Our concern here is mechanics, which is the motion of billiard balls and trucks and marbles and whatnot. You will find out that the laws of physics for this entire semester can be written down on the back of an envelope. A central purpose of this course is to show you repeatedly that starting with those few laws, you can deduce everything. I would encourage you to think the way physicists do, even if you don’t plan to be a physicist. The easiest way to master this subject is to follow the reasoning I The Structure of Mechanics 3 give you. That way, you don’t have to store too many things in your head. Early on, when there are four or five formulas, you can memorize all of them and you can try every one of them until something works, but, after a couple of weeks, you will have hundreds of formulas, and you cannot memorize all of them. You cannot resort to trial and error. You have to know the logic. The goal of physics is to predict the future given the present. We will pick some part of the universe that we want to study and call it “the system,” and we will ask, “What information do we need to know about that system at the initial time, like right now, in order to be able to predict its future evolution?” If I throw a piece of candy at you and you catch it, that’s an example of Newtonian mechanics at work. What did I do? I threw a piece of candy from my hand, and the initial conditions are where I released it and with what velocity. That’s what you see with your eyes. You know it’s going to go up, it’s going to follow some kind of parabola, and your hands get to the right place at the right time to receive it. That is an example of Newtonian mechanics at work, and your brain performed the necessary calculations effortlessly. You only have to know the candy’s initial location and the initial velocity. The fact that it was blue or red is not relevant. If I threw a gorilla at you, its color and mood would not matter. These are things that do not affect the physics. If a guy jumps off a tall building, we want to know when, and with what speed, he will land. We don’t ask why this guy is ending it all today; that is a question for the psych department. So we don’t answer everything. We ask very limited questions about inanimate objects, and we brag about how accurately we can predict the future. The Newtonian procedure for predicting the future, given the present, has two parts, kinematics and dynamics. Kinematics is a complete description of the present. It’s a list of what you have to know about a system right now. For example, if you’re talking about a piece of chalk, you will want to know where it is and how fast it’s moving. Dynamics then tells you why the chalk goes up, why it goes down, and so on. It comes down due to the force of gravity. In kinematics, you don’t ask for the reason behind anything. You simply want to describe things the way they are, and then dynamics tells you how and why that description changes with time. I’m going to illustrate the idea of kinematics by following my preferred approach: starting with the simplest possible example and slowly adding bells and whistles to make it more and more complicated. In the 4 The Structure of Mechanics initial stages, some of you mig ...
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Special Relativity
Galilean and Newtonian relativity
The theory of special relativity, while often associated with Einstein's monumental work of 1905,
can be traced to Galileo and Newton. The Galileo and Newton theory describes the motion of
objects with respect to a reference frame, which is identified as the particular observer. Newton 's
laws hold an inertial frame; it also holds a reference frame moving at a constant velocity. For
example, in a train, an observer who was asleep at the start of the journey and wakes in the middle
of the trip as the train moves cannot observe any changes. As such, if newton’s law is valid, the
inertial observer will not see any changes.
Not all observers and frames are inertial. For example, the equation of 𝑓 = 𝑚𝑎 is not true
in an accelerating train. For instance, in a non-inertial frame, the observer will notice motion or
movement when a train is accelerating or about to stop. The concept of Galilean transformation
considers the movement of objects at a constant velocity. According to this transformation, and
the enacted force causes an object to move. For example, find two trains running at a similar speed.
The force acting on both passengers is in both frames. Since both objects are in an identical
structure, the observer can notice the relative motion but cannot identify which train, in particular,
is moving.
Michelson and Morley and the ether
Michelson and Morley experimented to determine if the speed of light is equated as c—v to assess
the presence of substance referred to as the ether. The experiment obtained a result of a speed of
exactly c. From the research, Michelson and Morley found a negative effect where there was no
significant difference between the speed of light in motion through the presumed ether.

Postulates of Special Relativity
The most significant Postulates Einstein's special relativity include; All inertial observers
are equivalent, and the velocity of light is independent of the state of motion of the source and the
observer. In the first postulate, the concept of "equivalent" takes the total weight of the statement.
In this postulate, each inertial observer has an equal level of privileges in discovering the laws of
nature. For example, person A and person B, both inertial observers, are allowed to make claims.
Person A can claim that he or she is moving, and person B is at rest. Person B, on the other hand,
can equally argue that person A is at rest while he or she is moving. In the second postulate,
Einstein posits that if a light beam is emitted by a moving rocket, it travels and measures at c. As
such, all analysts will get a similar answer.
The Lorentz Transformation
The Lorentz Transformation supersedes the Galilean transformation. The measurement of space
and time actively identifies this concept. This transfor...

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