Stony Brook University
Academic Commons
Essential Graduate Physics Department of Physics and Astronomy
2024
Front Matter
Konstantin Likharev
SUNY Stony Brook, konstantin.likharev@stonybrook.edu
Follow this and additional works at: https://commons.library.stonybrook.edu/egp
Part of the Physics Commons
Recommended Citation
Likharev, Konstantin, "Front Matter" (2024). Essential Graduate Physics. 1.
https://commons.library.stonybrook.edu/egp/1
This Book is brought to you for free and open access by the Department of Physics and Astronomy at Academic
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Konstantin K. Likharev
Essential Graduate Physics
Lecture Notes and Problems
2024
Essential Graduate Physics
Lecture Notes and Problems
© Copyright K. Likharev, 2013-2024
Open access to this material is provided online; currently, at three mirror sites:
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The above copyright and license do not cover the figures adapted from published
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1 To the best of the author’s knowledge, the fair use clause of the U.S. copyright law (see,
e.g., http://www.copyright.gov/fls/fl102.html) allows viewing, browsing, and/or
downloading copyrighted materials for temporary, non-commercial, personal purposes,
without requesting the copyright holder’s permission.
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Essential Graduate Physics K. Likharev
Short Preface
(for all prospective readers)
1. Contents: This series consists of four subject parts: 2
CM: Classical Mechanics (for a 1-semester course),
EM: Classical Electrodynamics (2 semesters),
QM: Quantum Mechanics (2 semesters), and
SM: Statistical Mechanics (1 semester),
and also includes two common appendices:
MA: Selected Mathematical Formulas (16 pp.) and
UCA: Selected Units and Constants (4 pp.),
a common list of References (2 pp.), and the Front Matter you are reading now, including two prefaces,
the list of used notation, and the general list of contents.
2. Problems: Each chapter of the lecture notes ends with a list of exercise problems. Detailed
model solutions of these problems are available for free download from
https://essentialgraduatephysics.org/.
3. Hard copies: Besides free online access to all materials of the series, their B/W paperback
copies (one lecture notes volume and one problem solutions volume for each subject part, plus a
common Front Matter and Appendices brochure) are also available on Amazon.com:
https://www.amazon.com/stores/page/DAA96D04-4C1B-414C-B3E6-2F1E934A9561
for the lowest prices covering the printing costs and the distributor’s charges.
4. Basic distinctive features of the series:
—succinct lecture notes: ~200 pp. per semester;
—focus on problem-solving skills: almost 1,200 solved problems;
—extensive cross-referencing between the parts.
5. Precursors: Introductory university/college courses on physics and mathematics.3 (An
additional undergraduate-level course on each subject to be studied is a plus but not an absolute must.)
6. Goal final level: Sufficient to pass the corresponding course and comprehensive PhD exams
in a highly-ranked university.
Enjoy!
2 Their texts are saved as separate pdf files of each chapter and each appendix, optimized for two-page viewing
and double-side printing. Merged files for each part and the series as a whole, which are especially convenient for
search purposes, are also provided.
3 The math preparation of the reader should be sufficient to understand (but not necessarily remember!) the
formulas listed in the MA appendix.
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Detailed Preface
(for prospective instructors and other thorough readers)
1. Motivation and History
The series is a by-product of the so-called core physics courses I taught in the Department of
Physics and Astronomy of Stony Brook University from 1991 to 2013. Reportedly, most other physics
departments also require their graduate students to either take a set of similar courses, or pass
comprehensive exams based on an approximately similar body of knowledge, or both. This is why I
hope that my materials may be useful for instructors and students of such courses, as well as for
individual learners. All four subject parts of the series share a common teaching style, structure, and
notation, and are interlinked by extensive cross-referencing.
The motivation for composing the lecture notes and their distribution to my Stony Brook
students was my inability to find textbooks I could, with a clear conscience, use for teaching. First, the
good books I could find 4 did not quite match my class audiences, which included not only theory-
oriented but also experiment-oriented students, some PhD candidates from other departments, some
college graduates with substandard undergraduate backgrounds, and a few advanced undergraduates.
Second, for the rigid time restrictions imposed on the core physics courses, most available textbooks are
way too long, and using them would mean hopping from one topic to another, picking up a chapter here
and a section there, at a high risk of losing the necessary background material and logical connections
between course components – and students’ interest with them.5,
The main objective of these materials is to make students familiar with the basic notions and
ideas of physics that, in my humble view, have to be necessary parts of every professional physicist’s
education – hence the title of the series. As a backside of such a limited goal, I believe that my texts may
be used by advanced undergraduate physics students as well. Moreover, I hope that some parts of the
series may be useful for graduate students of other disciplines, including astronomy, chemistry,
electrical, computer, and electronic engineering, mechanical engineering, and material science.
Of course, real mastering a new concept or method is impossible without the skills to apply it to
particular situations. This is why in this series, a heavy accent is made on problem solution. In
particular, the introduction of every new theoretical technique is always accompanied by an application
4 In addition to the textbooks listed in References, several high-quality graduate-level teaching materials are now
freely available online, including (but not limited to) R. Fitzpatrick’s Classical Electromagnetism
(farside.ph.utexas.edu/teaching/jk1/Electromagnetism.pdf), M. Fowler’s Graduate Quantum Mechanics Lectures
(http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/home.html), B. Simons’ lecture notes on Advanced
Quantum Mechanics (www.tcm.phy.cam.ac.uk/~bds10/aqp.html), and D. Tong’s lecture notes on several topics
(www.damtp.cam.ac.uk/user/tong/teaching.html).
5 At the same time, many graduate-level textbooks lack even brief discussions of several traditional and modern
topics that I deem essential. To list just a few: statics and dynamics of elastic and fluid continua, basic notions of
physical kinetics, turbulence and deterministic chaos, physics of reversible and quantum computation, energy
relaxation and dephasing of open quantum systems, the van der Pol method (a.k.a. the Rotating-Wave
Approximation, RWA) in classical and quantum mechanics, electrons and holes in semiconductors, the weak-
potential and tight-binding approximations in the energy band theory, optical fiber electrodynamics, macroscopic
quantum effects in Bose-Einstein condensates, Bloch oscillations and Landau-Zener tunneling, cavity QED, and
the Density Functional Theory (DFT). All these topics are discussed, if only concisely, in these notes.
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Essential Graduate Physics K. Likharev
example or two. Additional exercise problems are listed at the end of each chapter of the lecture notes;
they may be used by instructors for homework assignments. Individual readers are strongly encouraged
to solve as many of these problems as possible.6
Supplements with detailed model solutions of the exercise problems are also available online –
for the link, see the Short Preface above. Sets of shorter problems suitable for tests, also with model
solutions, are available for university instructors from the author – also free of charge, but in return for a
signed commitment to avoid their unlimited distribution.7
A preliminary (“beta”) version of this series was placed into open online access in early 2014.
Since that time, its popularity has been steadily growing – possibly, facilitated by my continuous editing
of the material and adding more problems. As a result, during the 2023/24 academic year, readers from
130+ countries all over the globe downloaded more than 30,000 files of these materials from just the
basic website of the series – see the graphics below.8 Let me hope that this “final”9 version of Essential
Graduate Physics would earn an even broader readership.
SBU Academic Commons
(http://commons.library.stonybrook.edu/egp/)
(“additional files” are those of separate
chapters and appendices)
6 The problems that require either longer calculations or more creative approaches (or both) are marked by
asterisks.
7 Approximate contents of the request (to be sent to klikharev@gmail.com from a valid university address):
Dear Dr. Likharev,
I plan to use your lecture notes and problems of the Essential Graduate Physics series, part select: CM,
EM, QM, SM, in my course title during semester, year in department, university. I would appreciate your
sending me the Test Problems with Model Solutions for that part. I will avoid unlimited distribution of these
problems, in particular their posting on externally searchable websites. If I distribute the problems among my
students, I will ask them to adhere to the same restraint. I will let you know of any significant typos/deficiencies I
may find.
Sincerely, full name, university position, work phone number
8 A very early (and, admittedly, rather buggy) version of these materials was published in 2017-2019 by IOP as
eight volumes under the general title Essential Advanced Physics. Since then, the series has been significantly
extended and much better corrected and edited.
9 My current plans are to continue its improvement, though probably at a slower pace than before.
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Essential Graduate Physics K. Likharev
2. Disclaimer
Since these materials are available online free of charge, and that their author is not getting any
royalties from the sale of their paperback copies, it is hard to imagine somebody blaming him for
deceiving “customers” for his commercial gain. Still, I would like to go a little bit beyond the usual
litigation-avoiding statements,10 and offer a word of caution to potential readers, to preempt their
possible disappointment.
(i) These are NOT courses of theoretical physics in the contemporary sense of this term. Though
much of the included material is very similar to that in older textbooks on “theoretical physics” (most
notably, in the famous series by L. Landau and E. Lifshitz), my focus is on the basic concepts and ideas
of physics and their most important applications, rather than on sophisticated theoretical techniques.
Indeed, the set of theoretical methods discussed in the notes is limited to the minimum needed for
quantitative formulations of the key notions of physics and applying them to baseline system models, as
exemplified the examples and problems included in the series. Moreover, because of the time/space
limits, I have not been able to cover some important fields of theoretical physics – most regretfully,
general relativity,11 and also quantum field theory (beyond the basic quantum electrodynamics discussed
in QM Chapter 9). As a result, if you want to work in modern theoretical physics research, you need to
know much more than what this series teaches.
(ii) My lecture notes are NOT textbooks – at least not the usual ones. A usual textbook tries
(though most commonly fails) to cover virtually all aspects of the addressed field. As a result, it is
typically way too long to be fully read and understood by students during the time allocated for the
corresponding course. In contrast, my lecture notes are quite succinct – about 200 pages per semester,
enabling their thorough reading. This briefness is partly compensated by a large number of problems,
with some of them devoted to additional topics, so their solutions may serve as extensions of the lecture
notes. I also give extensive further reading recommendations on the topics I had no time/space to cover.
To summarize again, what my materials (including the problem solutions) really ARE is a
description of the physics’ hard core that has to be mastered by everybody who wants to work in the
field – whether it is in theory or experiment, fundamentals or applications.
3. Confessions
First, I have to confess that besides giving an introduction to the core of physics, my course
series also had another goal: to convey my own enchantment by the unparalleled beauty of the basic
concepts and ideas of this science, and the remarkable logic of their fusion into a wonderful single
construct, which is only conditionally partitioned by the subject boundaries. (Hence so many cross-
references between the parts.)
One more confession: I know very well that my texts are far from being perfect. While I have
made a major effort to organize the material so that the students could readily follow and enjoy the
10 Yes, Virginia, these notes represent only my personal opinions, not necessarily those of the Department of
Physics and Astronomy of Stony Brook University, the SBU at large, the SUNY system as a whole, the Empire
State of New York, the US federal agencies and private companies that funded my group’s research, etc. No, dear,
I cannot be held responsible for any harm, either bodily or mental, their reading may (?) cause.
11 For an introduction to that subject, I can recommend either its review by S. Carroll, Spacetime and Geometry,
Addison-Wesley, 2003, or a longer text by A. Zee, Einstein Gravity in a Nutshell, Princeton U. Press, 2013.
Front Matter vi
Essential Graduate Physics K. Likharev
narrative, it is more than possible that, at least in some instances, I have not quite reached this goal. In
addition, it is almost certain that despite all my efforts and the great help from my colleagues, students,
teaching assistants, and some readers, listed below, not all typos (and possibly, even real errors) have
been weeded out.
This is why all (however candid) remarks and suggestions by the readers would be highly
appreciated; they may be sent to klikharev@gmail.com. All significant contributions will be gratefully
acknowledged in future edits.
4. Acknowledgments
I am extremely grateful to my faculty colleagues and other readers who commented on certain
sections of the notes; here is their list (in the alphabetic order):12
A. Abanov, P. Allen, D. Averin, S. Berkovich, P.-T. de Boer, M. Fernandez-Serra,
R. F. Hernandez, P. Johnson, T. Konstantinova, A. Korotkov, V. Semenov, F. Sheldon,
S. Sridharan, E. Tikhonov, O. Tikhonova, E. Voronina, X. Wang, T.-C. Wei.13
The Department of Physics and Astronomy of Stony Brook University was very responsive to
my kind requests for certain time ordering of my teaching assignments, which was beneficial for note
writing and editing. The department, and the university as a whole, also provided a very friendly general
environment for my work there for almost three decades.
A large part of my scientific background and research experience reflected in these materials
came from my education and work in the Department of Physics of Moscow State University.
And last but not least, I am very grateful to my wife Lioudmila for several good bits of advice on
aesthetic aspects of note typesetting, and more importantly, for all her love, care, and patience – without
them, this writing project would be impossible.
K. K. Likharev
https://you.stonybrook.edu/likharev/
June 2024
12 I am very sorry that I have not kept proper records from the beginning of my lectures at Stony Brook, so I
cannot list all the numerous students and TAs who had kindly attracted my attention to typos in earlier versions of
these notes. Needless to say, I am very grateful to them all as well.
13 Obviously, these kind people are not responsible for the remaining deficiencies.
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Notation
Abbreviations Fonts Symbols
Eq. any displayed formula F, F scalar variables14,15 time differentiation (d/dt)
Fig. figure F, F vector variables spatial differentiation vector (del)
Sec. section F̂ , Fˆ scalar operators approximately equal to
c.c. complex conjugate F̂, Fˆ vector operators ~ of the same order as
h.c. Hermitian conjugate F matrix proportional to
Fjj’ matrix element equal to by definition (or evidently)
Subject parts of the series scalar (“dot-”) product
CM: Classical Mechanics vector (“cross-”) product16
EM: Classical Electrodynamics time averaging
QM: Quantum Mechanics statistical averaging
SM: Statistical Mechanics [ , ] commutator
Appendices { , } anticommutator17
MA: Selected Mathematical Formulas n unit vector
UCA: Selected Units and Constants
Frames
In the lecture notes, the most general and/or important formulas are highlighted with blue frames
and short titles on the margins.
Numbering
Chapter numbers are dropped in all references to formulas, figures, footnotes, and problems
within the same chapter.
Prime signs
In most cases, the prime signs (′, ″, etc.) are used to distinguish similar variables or indices (such
as j and j′ in the matrix element above), rather than to denote derivatives.
14 The same letter, if typeset in different fonts, typically denotes different variables.
15 In the plain text, Italic fonts are used for emphasis – in particular, of the new terms at their first usage.
16 On a few occasions, the cross sign is used to emphasize the usual multiplication of scalars.
17 Following a venerable tradition, the curly brackets (“braces”) are also used to enclose the exponential function
arguments if they are typeset inline, e.g., exp{–x/ }.
Front Matter viii
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General Table of Contents
(besides this Front Matter)
Exercise
CM: Classical Mechanics Pages Problems
Table of Contents and Introductory Remarks 4 –
Chapter 1. Review of Fundamentals 14 14
Chapter 2. Lagrangian Analytical Mechanics 14 11
Chapter 3. A Few Simple Problems 22 27
Chapter 4. Rigid Body Motion 32 37
Chapter 5. Oscillations 38 22
Chapter 6. From Oscillations to Waves 30 26
Chapter 7. Deformations and Elasticity 38 23
Chapter 8. Fluid Mechanics 30 27
Chapter 9. Deterministic Chaos 14 5
Chapter 10. A Bit More of Analytical Mechanics 16 10
Lecture Notes and Problems Total 252 202
Supplement: Exercise Problems with Model Solutions 304 202
Additional file (available for course instructors upon request): Pages Problems
Test Problems with Model Solutions 42 45
Exercise
EM: Classical Electrodynamics Pages Problems
Table of Contents and Introductory Remarks 4 –
Chapter 1. Electric Charge Interaction 20 20
Chapter 2. Charges and Conductors 68 47
Chapter 3. Dipoles and Dielectrics 28 30
Chapter 4. DC Currents 16 15
Chapter 5. Magnetism 42 29
Chapter 6. Electromagnetism 38 31
Chapter 7. Electromagnetic Wave Propagation 70 43
Chapter 8. Radiation, Scattering, Interference, and Diffraction 38 28
Chapter 9. Special Relativity 56 42
Chapter 10. Radiation by Relativistic Charges 40 15
Lecture Notes and Problems Total 420 300
Supplement: Exercise Problems with Model Solutions 426 300
Additional file (available for course instructors upon request): Pages Problems
Test Problems with Model Solutions 46 52
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Exercise
QM: Quantum Mechanics Pages Problems
Table of Contents and Introductory Remarks 4 –
Chapter 1. Introduction 26 18
Chapter 2. 1D Wave Mechanics 76 47
Chapter 3. Higher Dimensionality Effects 64 49
Chapter 4. Bra-ket Formalism 52 36
Chapter 5. Some Exactly Solvable Problems 48 55
Chapter 6. Perturbative Approaches 36 31
Chapter 7. Open Quantum Systems 54 17
Chapter 8. Multiparticle Systems 52 35
Chapter 9. Introduction to Relativistic Quantum Mechanics 36 22
Chapter 10. Making Sense of Quantum Mechanics 16 1
Lecture Notes and Problems Total 464 311
Supplement: Exercise Problems with Model Solutions 522 311
Additional file (available for course instructors upon request): Pages Problems
Test Problems with Model Solutions 61 68
Exercise
SM: Statistical Mechanics Pages Problems
Table of Contents and Introductory Remarks 4 –
Chapter 1. Review of Thermodynamics 24 18
Chapter 2. Principles of Physical Statistics 44 36
Chapter 3. Ideal and Not-So-Ideal Gases 34 30
Chapter 4. Phase Transitions 36 24
Chapter 5. Fluctuations 44 30
Chapter 6. Elements of Kinetics 38 18
Lecture Notes and Problems Total 224 156
Supplement: Exercise Problems with Model Solutions 252 156
Additional file (available for course instructors upon request): Pages Problems
Test Problems with Model Solutions 25 26
Appendices Pages
MA: Selected Mathematical Formulas 16
UCA: Selected Units and Constants 4
References Pages
A partial list of books used at work on the series 2
Front Matter x
