Conquering the physics GRE: reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2018
|
| Edition: | Third edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xiii, 282 Seiten Diagramme |
| ISBN: | 9781108409568 |
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Record in the Search Index
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| adam_text | CONTENTS
Preface page ix 1.7 Springs and Harmonic Oscillators 22
How to Use This Book xi 1.7.1 Normal Modes 23
Resources xii 1.7.2 Damping, Driving, and Resonance 24
1.7.3 Further Examples 25
1.7.4 Problems: Springs 27
1 1.8 Fluid Mechanics 27
Classical Mechanics 1 1.8.1 Bernoulli s Principle 27
1.8.2 Buoyant Forces 29
1.1 Blocks 1 1.8.3 Problems: Fluid Mechanics 29
1.1.1 Blocks on Ramps 1 1.9 Solutions: Classical Mechanics 29
1.1.2 Falling and Hanging Blocks 2
1.1.3 Blocks in Contact 3
1.1.4 Problems: Blocks 3 2
1.2 Kinematics 5
1.2.1 Circular Motion 5 Electricity and Magnetism 35
1.2.2 Problems: Kinematics 6 2.1 Electrostatics 35
1.3 Energy 7 2.1.1 Maxwells Equations for Electrostatics 35
1.3.1 Types of Energy 7 2.1.2 Electric Potential 35
1.3.2 Kinetic/Potential Problems 8 2.1.3 Integral Form of Maxwells Equations 36
1.3.3 Rolling Without Slipping 9 2.1.4 Standard Electrostatics Configurations 37
1.3.4 Work-Energy Theorem 11 2.1,5 Boundary Conditions 38
1.3.5 Problems: Energy 11 2.1.6 Conductors 40
1.4 Momentum 12 2.1.7 Method of Images 40
1.4.1 Linear Collisions 12 2.1.8 Work and Energy in Electrostatics 42
1.4.2 Rotational Motion and Angular Momentum 12 2.1.9 Capacitors 43
1.4.3 Moment of Inertia 14 2.1.10 Problems: Electrostatics 44
1.4.4 Center of Mass 15 2.2 Magnetostatics 45
1.4.5 Problems: Momentum 15 2.2.1 Basic Tools 45
1.5 Lagrangians and Hamiltonians 16 2.2.2 Ampères Law and the Biot-Savart Law 46
1.5.1 Lagrangians 16 2.2.3 Standard Magnetostatics Configurations 46
1.5.2 Euler-Lagrange Equations 17 2.2.4 Boundary Conditions 48
1.5.3 Hamiltonians and Hamilton’s Equations 2.2.5 Work and Energy in Magnetostatics 48
of Motion 18 2.2.6 Cyclotron Motion 48
1.5.4 Problems: Lagrangians and Hamiltonians 19 2.2.7 Problems: Magnetostatics 49
1.6 Orbits 19 2.3 Electrodynamics 49
1.6.1 Effective Potential 19 2.3.1 Maxwells Equations 49
1.6.2 Classification of Orbits 20 2.3.2 Faradays Law 50
1.6.3 Keplers “Laws” 21 2.3.3 Inductors 50
1.6.4 Problems: Orbits 22 2.3.4 Problems: Electrodynamics 51
Contents
2.4 Dipoles
2.4.1 Electric Dipoles
2.4.2 Magnetic Dipoles
2.4.3 Multipole Expansion
2.4.4 Problems: Dipoles
2.5 Matter Effects
2.5.1 Polarization
2.5.2 Dielectrics
2.5.3 Problems: Matter Effects
2.6 Electromagnetic Waves
2.6.1 Wave Equation and Poynting Vector
2.6.2 Radiation
2.6.3 Problems: Electromagnetic Waves
2.7 Circuits
2.7.1 Basic Elements
2.7.2 Kirchhoffs Rules
2.7.3 Energy in Circuits
2.7.4 Standard Circuit Types
2.7.5 Problems: Circuits
2.8 Solutions: Electricity and Magnetism
3
Optics and Waves
3.1 Properties of Waves
3.1.1 Wave Equation
3.1.2 Nomenclature and Complex Notation
3.1.3 Dispersion Relations
3.1.4 Examples of Waves
3.1.5 Index of Refraction
3.1.6 Polarization
3.2 Interference and Diffraction
3.2.1 Double-Slit Interference
3.2.2 Single-Slit Diffraction
3.2.3 Optical Path Length
3.2.4 Thin Films and Phase Shifts
3.2.5 Miscellaneous Diffraction
3.3 Geometric Optics
3.3.1 Reflection and Refraction
3.3.2 Lenses and Mirrors
3.4 Assorted Extra Topics
3.4.1 Rayleigh Scattering
3.4.2 Doppler Effect
3.4.3 Standing Sound Waves
3.5 Problems: Optics and Waves
3.6 Solutions: Optics and Waves
4
Thermodynamics and Statistical Mechanics
4.1 Basic Statistical Mechanics
4.1.1 Ensembles and the Partition Function
4.1.2 Entropy
52 4.1.3 Classical Limit 80
52 4.1.4 Equipartition Theorem 80
52 4.1.5 Some Combinatorial Facts 80
53 4.2 Thermodynamics 80
53 4.2.1 Three Laws 81
53 4.2.2 Gases and Equations of State 82
54 4.2.3 Types of Processes 82
54 4.2.4 Relations Between Thermodynamic Variables 84
54 4.2.5 Heat Capacity 84
54 4.2.6 Model Systems 85
54 4.3 Quantum Statistical Mechanics 87
56 4.4 Problems: Thermodynamics and Statistical
56 Mechanics 88
56 4.5 Solutions: Thermodynamics and Statistical
57 Mechanics 90
57
57 5
58
58 Quantum Mechanics and Atomic Physics 92
59 5.1 Formalism (Ffow To Calculate) 92
5.1.1 Wavefunctions and Operators 92
5.1.2 Dirac Notation 94
5.1.3 Schrodinger Equation 95
63 5.1.4 Commutators and the Uncertainty Principle 96
63 5.1.5 Problems: Formalism 98
63 5.2 Harmonic Oscillator 99
63 5.2.1 One Dimension 99
65 5,2.2 Three Dimensions 100
65 5.2,3 Problems: Harmonic Oscillator 101
65 5.3 Other Standard Hamiltonians 101
66 5.3.1 Infinite Square Well 101
67 5.3.2 Free Particle 102
67 5.3.3 Delta Function 102
68 5.3.4 Finite Square Well 103
68 5.3.5 Scattering States: Reflection and Transmission 103
69 5.3.6 Problems: Other Standard Hamiltonians 104
70 5.4 Quantum Mechanics in Three Dimensions 104
70 5.4.1 Radial Equation and Effective Potential 105
70 5.4.2 Angular Momentum and Spherical Harmonics 105
71 5.4.3 The Hydrogen Atom 106
72 5.4.4 Problems: Quantum Mechanics in Three
72 Dimensions 108
72 5.5 Spin 108
73 5.5.1 Spin-1/2 108
74 5.5.2 Spin and the Wavefunction 109
rjr 5.5.3 Adding Spins 110
JO 5.5.4 Bosons and Fermions 111
5.5.5 Problems: Spin 112
5.6 Approximation Methods 113
78 5.6.1 Time-Independent Perturbation Theory:
First and Second Order 113
78 5.6.2 Variational Principle 114
78 5.6.3 Adiabatic Theorem 114
79 5.6.4 Problems: Approximation Methods 114
Contents
vii
V________
5.7 Atomic Physics Topics 115
5.7.1 Bohr Model 115
5.7.2 Perturbations to Hydrogen Atoms 115
5.7.3 Shell Model and Electronic Notation 116
5.7.4 Stark and Zeeman Effects 116
5.7.5 Selection Rules 117
5.7.6 Blackbody Radiation 117
5.7.7 Problems: Atomic Physics Topics 118
5.8 Solutions: Quantum Mechanics and Atomic
Physics 119
6
Special Relativity 123
6.1 Relativity Basics 123
6.1.1 Simultaneity 124
6.1.2 Time Dilation 124
6.1.3 Lorentz Contraction 124
6.1.4 Velocity Addition 125
6.2 4-Vectors 125
6.2.1 Lorentz Transformation Matrices 125
6.2.2 Relativistic Dot Product 126
6.3 Relativistic Kinematics 127
7.6 Problems: Laboratory Methods 143
7.7 Solutions: Laboratory Methods 145
8
Specialized Topics 146
8.1 Nuclear and Particle Physics 146
8.1.1 The Standard Model: Particles and
Interactions 146
8.1.2 Nuclear Physics: Bound States 147
8.1.3 Symmetries and Conservation Laws 148
8.1.4 Recent Developments 149
8.2 Condensed Matter Physics 149
8.2.1 Crystal Structure 149
8.2.2 Electron Theory of Metals 150
8.2.3 Semiconductors 151
8.2.4 Superconductors 151
8.3 Astrophysics 152
8.4 Recent Nobel Prizes 153
8.5 Problems: Specialized Topics 155
8.6 Solutions: Specialized Topics 157
6.3.1 Conserved vs. Invariant 127
6.3.2 Exploiting the Invariant Dot Product 128
6.4 Miscellaneous Relativity Topics 129
6.4.1 Relativistic Doppler Shift 129
6.4.2 Pythagorean Triples 129
6.5 Relativity: What to Memorize 129
6.6 Problems: Special Relativity 130
6.7 Solutions: Special Relativity 131
7
Laboratory Methods 134
7.1 Graph Reading 134
7.1.1 Dimensional Analysis 134
7.1.2 Log Plots 134
7.2 Statistics 135
7.2.1 Error Analysis 135
7.2.2 Poisson Processes 136
7.3 Electronics 136
7.3.1 AC Behavior of Basic Circuit Elements 136
7.3.2 More Advanced Circuit Elements 138
7.3.3 Logic Gates 138
7.4 Radiation Detection and Instrumentation 139
7.4.1 Interaction of Charged Particles with Matter 139
7.4.2 Photon Interactions 140
7.4.3 General Properties of Particle Detectors 141
7.4.4 Radioactive Decays 141
7.5 Lasers and Interferometers 141
7.5.1 Generic Laser Operation 141
7.5.2 Types of Lasers 142
7.5.3 Interferometers 143
9
Special Tips and Tricks for the Physics GRE 159
9.1 Derive, Don’t Memorize 159
9.2 Dimensional Analysis 160
9.3 Limiting Cases 161
9.4 Numbers and Estimation 162
9.5 Answer Types (What to Remember in a Formula) 163
9.6 General Test-Taking Strategies 165
9.7 Problems: Tips and Tricks 165
9.8 Solutions: Tips and Tricks 166
Sample Exams and Solutions 167
Sample Exam 1 169
Sample Exam 2 187
Sample Exam 3 209
Answers to Sample Exam 1 227
Answers to Sample Exam 2 228
Answers to Sample Exam 3 229
Solutions to Sample Exam 1 230
Solutions to Sample Exam 2 243
Solutions to Sample Exam 3 254
References 267
Equation Index 268
Subject Index 276
Problems Index 280
Conquering the Physics GRE
Third Edition
The Physics GRE plays a significant role in deciding admissions to nearly all US physics
Ph.D. programs, yet few exam-prep books focus on the tests actual content and unique
structure. Recognized as one of the best student resources available, this tailored guide
has been thoroughly updated for the current Physics GRE. It contains carefully selected
review material matched to all of the topics covered, as well as tips and tricks to help you
solve problems under time pressure. It features three full-length practice exams, revised
to accurately reflect the difficulty of the current test, with fully worked solutions so that
you can simulate taking the test, review your preparedness, and identify areas in which
further study is needed. Written by working physicists who took the Physics GRE for
their own graduate admissions to MIT, this self-contained reference guide will help you
achieve your best score.
Yoni Kahn is a theoretical physicist researching dark matter and supersymmetry. A post-
doctoral research associate at Princeton University, he obtained his Ph.D. from MIT
in 2015 and in 2016 received the American Physical Society’s J.J. and Noriko Sakurai
Dissertation Award in Theoretical Particle Physics.
Adam Anderson is an experimental physicist working at the interface between cos-
mology and particle physics. He received his Ph.D. from MIT in 2015 and is now
a Lederman postdoctoral fellow at Fermi National Accelerator Laboratory, develop-
ing instruments for performing precision measurements of the cosmic microwave
background.
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| spelling | Kahn, Yonatan Verfasser (DE-588)1177730219 aut Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions Yoni Kahn (Princeton University, New Jersey), Adam Anderson (Fermilab, Batavia, Illinois) Third edition Cambridge Cambridge University Press 2018 xiii, 282 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Physics / Examinations, questions, etc Graduate Record Examination / Study guides Anderson, Adam Verfasser (DE-588)1177735520 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030534830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030534830&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kahn, Yonatan Anderson, Adam Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions Physics / Examinations, questions, etc Graduate Record Examination / Study guides |
| title | Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions |
| title_auth | Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions |
| title_exact_search | Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions |
| title_full | Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions Yoni Kahn (Princeton University, New Jersey), Adam Anderson (Fermilab, Batavia, Illinois) |
| title_fullStr | Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions Yoni Kahn (Princeton University, New Jersey), Adam Anderson (Fermilab, Batavia, Illinois) |
| title_full_unstemmed | Conquering the physics GRE reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions Yoni Kahn (Princeton University, New Jersey), Adam Anderson (Fermilab, Batavia, Illinois) |
| title_short | Conquering the physics GRE |
| title_sort | conquering the physics gre reviews all of the topics covered in the physics gre gives tips and techniques to help solve problems more quickly includes three full length practice exams with worked solutions |
| title_sub | reviews all of the topics covered in the Physics GRE ; gives tips and techniques to help solve problems more quickly ; includes three full-length practice exams with worked solutions |
| topic | Physics / Examinations, questions, etc Graduate Record Examination / Study guides |
| topic_facet | Physics / Examinations, questions, etc Graduate Record Examination / Study guides |
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