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1000 solved problems in classical physics : an exercise book

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• 1D and 2D Kinematics.- Statics and Particle Dynamics.- Rotational Kinematics.- Rotational Dynamics.- Gravitation.- Oscillations.- Lagrange and Hamilton Dynamics.- Waves.- Fluid Dynamics.- Phases of Matter.- Thermal Physics.- Electrostatics.- Electric Circuits.- Electromagnetism.- Optics.
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1000 Solved Problems in Modern Physics

• © 2010
• Ahmad A. Kamal 0

Murphy, USA

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Excercise book for physics students

Guide for teachers when preparing exams

Covers a large part of physics lectures except optics

Well chosen and didactically solved problems to physics courses

Useful to students to deepen their knowledge

Contains summaries and formulas with explanatory notes

The book is based mainly on the actual question papers for undergraduate and graduate students

The problems have a large variety and are not necessarily of plug-in-type and explain the underlying physics

Summaries and formulas with explanatory notes

Includes supplementary material: sn.pub/extras

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Table of contents (10 chapters)

Front matter, mathematical physics.

Ahmad A. Kamal

Quantum Mechanics – I

Quantum mechanics – ii, thermodynamics and statistical physics, solid state physics, special theory of relativity, nuclear physics – i, nuclear physics – ii, particle physics – i, particle physics – ii, back matter.

• Atomic and molecular physics
• Exercise and solution book physics
• Nuclear physics
• Nuclear physics problems solved
• Particle physics problems solved
• Physics exercises solved
• Quantum mechanics
• Solid state physics
• Theoretical physics
• mathematical physics

About this book

From the reviews:

“The book provides a collection of problems and solutions in physics targeting mainly undergraduate students. … The book focuses mainly on basic problems in quantum mechanics, nuclear physics and particle physics. … the book could be a useful addition to problem and solution books in physics for undergraduate students.” (Willi-Hans Steeb, zbMATH, Vol. 1271, 2013)

Authors and Affiliations

About the author.

The author obtained his Doctoral degree from University of Bristol, U.K. under the supervision of Emeritus Professor Dr.D.H. Perkins, FRS. The author has worked in high-energy physics for a number of years using photographic emulsions exposed at CERN. He has also used low-energy facilities at Nuclear Science Center at New Delhi. He was a postdoctoral fellow at the University of Ottawa, visitor to CERN, visiting professor at the University of Tebrez. He has published 40 research papers in International Journals and gave lectures on Nuclear physics, particle physics, quantum mechanics, classical mechanics, mathematical physics, atomic and molecular physics and relativity at undergraduate and graduate levels at various universities for several years. He was a Professor and Head of the Department of Physics and Chairman, Board of studies at the Osmania University.

Theory of everything: how a fear of failure is hampering physicists’ quest for the ultimate answer

Tutor and researcher in Philosophy of Science, Manchester Metropolitan University

Disclosure statement

Sam McKee does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

Manchester Metropolitan University provides funding as a member of The Conversation UK.

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It has been over a century since the boom period of physics exploded with Albert Einstein, Max Planck and others, sending us spinning into a new world of chaos from our previously ordered universe. This brilliant generation of physicists ultimately peeled back the layers of the universe, as well as of the atom, to reveal a world stranger than fiction.

Ever since those earliest days of quantum mechanics, the theory ruling the microworld of atoms and particles, the holy grail of physics has been finding a theory of everything – uniting quantum mechanics with Einstein’s theory of general relativity, which applies to the universe on large scales.

But we still don’t have a tried and tested theory of everything. And I believe a fear of failure is a big part of the problem.

Creating a theory of everything isn’t exactly easy. It involves producing one framework uniting the fundamental forces of our universe, while accounting for all the underlying constants and quantities as well as every subatomic particle. The prize for whoever answers this ultimate question is eternal glory in the annals of humankind.

There was great hunger to solve it in Einstein’s generation. In fact, Einstein worked on a theory of everything on his very deathbed – work that he was ultimately ridiculed for. Einstein’s contribution to physics was so great he still remains a superstar. But physicists Arthur Eddington, Hermann Weyl and mathematician David Hilbert were not so fortunate, with some facing much worse consequences.

Take Eddington, for example, perhaps the greatest scientist you have never heard of. The Cambridge astronomer and physicist proved Einstein correct in his work analysing a 1919 eclipse – launching Einstein to superstardom. Eddington also wrote the first English books on relativity before doing the same on Georges Lemaître’s Big Bang theory.

He also wrote a book on quantum physics , and became the greatest popular writer on science in the 1920s and 1930s, alongside his groundbreaking work on stellar physics (the physics of stars). Yet he is obscure today due to his intense pursuit of a fundamental theory.

Published posthumously, his attempt was immediately banished for its incredible failure. Mocked as numerology (the belief in a mystical relationship between a number and events), his strange interest in the power of certain numbers was made fun of by other scientists. And, as many notable astrophysicists have pointed out , it has produced no value since its publication.

Eddington’s stunning final failure served as a powerful warning of the price that comes with missing the mark. The final decade of his life spent pursuing a theory of everything ended in severe damage to his legacy.

A new generation

The generation of the physicist Richard Feynman (1918–88), following that of Einstein and Eddington, lost interest in a theory of everything. Feynman and his peers found their own glory in new subatomic discoveries and theories, and applications of physics to chemistry and biology, leading to several Nobel prizes. The ridicule endured by those who tried and failed before them may have been one of the reasons.

This inordinate cost for failure ultimately rose alongside the glory of interwar physics. In a period of unparalleled success, failure was more unforgiving. This was hardly an incentive for young and brilliant modern minds seeking to apply themselves to the largest question.

Even today, attempts at theories of everything get mocked. String theory, for example, is such an attempt, and has been scorned by Nobel laureate Roger Penrose as not being real science.

He is not alone. Physicist Stephen Hawking believed a version of string theory called M-theory was our best option for a theory of everything. But the theory has struggled in producing predictions that can be tested by experiments.

A young scientist today may wonder, if Einsteinx, Eddington and Hawking could not solve the problem, then who will? And indeed, many are doubtful that it can be achieved. Is it even necessary as, pragmatically, we can do without one?

It is no wonder, then, that many physicists prefer to avoid the term “theory of everything” these days, opting instead for less grandiose alternatives such as “quantum gravity”.

Funding and career progression

Alongside the heavy price of failure, other problems are lurking. A brilliant young mind could be staring at a career dead end in seeking out a theory of everything. What academic progression can one expect at the start of their career if this is desired? Who will give significant funding to young, unproven researchers pursuing a seemingly impossible goal in the short term?

It is likely that a theory of everything will ultimately require massive collaboration to be solved. Ironically, this may be a job for the older physicists, despite the warnings of Eddington and others. Francis Crick dedicated his attention to trying to solve the problem of consciousness in his later years, albeit without success.

We need collaboration. But we may be looking at the prospect of a theory of everything only coming from those who have accomplished so much they can afford the potential embarrassment and will be given the benefit of the doubt. This hardly stirs the enthusiasm of the vibrant, young minds that may otherwise tackle the problem.

In trying to solve the ultimate problem, we may have inadvertently created a monster. Our academic framework for research progression is not conducive to it, and history has presented an unkind picture of what happens to those who try.

And yet, our greatest progress has always come from those willing to take risks.

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Solving Fermi-Hubbard-type models by tensor representations of backflow corrections

Yu-tong zhou, zheng-wei zhou, and xiao liang, phys. rev. b 109 , 245107 – published 4 june 2024.

• No Citing Articles

The quantum many-body problem is an important topic in condensed matter physics. To efficiently solve the problem, several methods have been developed to improve the representation ability of wave functions. For the Fermi-Hubbard model under periodic boundary conditions, current state-of-the-art methods are neural network backflows and the hidden fermion Slater determinant. The backflow correction is an efficient way to improve the Slater determinant of free particles. In this work we propose a tensor representation of the backflow-corrected wave function; we show that for the spinless t − V model, the energy precision is competitive or even lower than current state-of-the-art fermionic tensor network methods. For models with spin, we further improve the representation ability by considering backflows on fictitious particles with different spins, thus naturally introducing nonzero backflow corrections when the orbital and the particle have opposite spins. We benchmark our method on molecules in the STO-3G basis and the Fermi-Hubbard model with periodic and cylindrical boundary conditions. We show that the tensor representation of backflow corrections achieves competitive or even lower-energy results than current state-of-the-art neural network methods.

• Received 12 March 2024
• Revised 12 May 2024
• Accepted 22 May 2024

DOI: https://doi.org/10.1103/PhysRevB.109.245107

©2024 American Physical Society

Physics Subject Headings (PhySH)

Authors & affiliations.

• 1 CAS Key Laboratory of Quantum Information, University of Science and Technology of China , Hefei 230026, China
• 2 Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China , Hefei 230026, China
• 3 Hefei National Laboratory, University of Science and Technology of China , Hefei 230088, China
• 4 Pittsburgh Supercomputing Center , Carnegie Mellon University , Pittsburgh, Pennsylvania 15213, USA
• 5 Department of Physics, Carnegie Mellon University , Pittsburgh, Pennsylvania 15213, USA
• * [email protected]
• † [email protected]

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Vol. 109, Iss. 24 — 15 June 2024

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The matrix in the Slater determinant for N particles, with N ↑ and N ↓ being the particle numbers for spin up and spin down, respectively. The spin on the horizontal (vertical) axis denotes the spin of the particles (orbitals).

The energy convergence of the first-order gradient descent for the spinless t − V model with V / t = 1 on the 10 × 10 lattice under the OBC. The MC sample number is 128 000, and the parameter updating step size δ = 5 × 10 − 4 . The converged energy per site is − 0.4617 , while the reference energy obtained by fPEPS is − 0.4620 .

Comparison of energies (per site) of two kinds of tensor representations of backflow corrections for the Fermi-Hubbard model with n = 0.875 and U = 8 on the 4 × L lattice with the PBC. “Original BW” denotes the coefficient c i j , and the HF orbitals are represented by two separate tensors. “BW” denotes the backflow-corrected wave function is represented by a single tensor. Each energy is evaluated by the p = 0 wave function.

Energy comparisons for the Fermi-Hubbard model on 4 × L lattices under the PBC and U = 8 . The filling is n = 0.875 . Red upward-pointing triangles denote NN backflow, green downward-pointing triangles denote HDFS. BW1 energy results of p = 0 ( p = 1 ) are denoted by left-pointing (right-pointing) triangles. BW2 energy results of p = 0 ( p = 1 ) are denoted by squares (circles).

Comparison of spin correlation functions 〈 S ( 0 , 0 ) S ( x , y ) 〉 for BW1 (solid line) and BW2 (dashed line) for different lattice sizes; the filling is n = 1 , and U = 8 . The relative distance is defined as d = x 2 + y 2 ; all results are evaluated with p = 1 wave functions.

The spin density of the Fermi-Hubbard model with filling n = 0.875 and U = 8 under the PBC, evaluated using the p = 1 wave function. On the 4 × 8 lattice, the spin density obtained with (a) BW1 and (b) BW2. The spin density on the 4 × 24 lattice obtained with (c) BW1 and (d) BW2.

The spin density and the hole density achieved with BW2 on rectangular lattices under (a)–(d) the CBC and (e) and (f) the PBC, with a pinning field applied on both short edges. (a) and (b) depict the 4 × 16 lattice, with filling n = 0.875 . (c) and (d) depict the 4 × 20 lattice, with filling n = 0.9 . (e) and (f) depict the 8 × 16 lattice, with filling n = 0.875 .

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The unexpected connection between brewing coffee and understanding turbulence

Unconventional use of statistical mechanics sheds light on how turbulence occurs.

In 1883 Osborne Reynolds injected ink into water in a short, clear pipe to observe its movement. His experiments showed that as the input water velocity increased, the flow went from laminar (smooth and predictable) to turbulent (unsteady and unpredictable) through the development of localized patches of turbulence, known today as "puffs." His work helped launch the field of fluid mechanics, but, as experiments often do, it raised more questions. For example, why do these transitions between laminar and turbulent flows occur and how can the transitions be characterized quantitatively?

Although Reynolds was not able to find the answer, an international team of researchers, led by University of California San Diego Chancellor's Distinguished Professor of Physics Nigel Goldenfeld and Björn Hof of the Institute of Science and Technology Austria have used statistical mechanics to solve this longstanding problem. Their work appears in Nature Physics .

One of the novelties of this work was that the team looked at the problem not only from the perspective of fluid mechanics, but also through statistical mechanics -- the branch of physics that uses mathematics to describe the behavior of systems with a large number of particles. Usually this is applied to systems in equilibrium, but turbulence is not in equilibrium, because energy is constantly moving in and out of the fluid. However, building on their earlier work, the team showed that fluids move through a pipe in a non-equilibrium phase transition, known as directed percolation, at the transition point between laminar and turbulent flow. If "percolation" makes you think of your morning coffee, it provides a useful example here.

A storm in a coffee cup

When coffee is percolating, water moves through coffee grounds at a certain rate and flows downward in the direction of gravity. This flow is known as directed percolation. Too fast and the coffee is weak; too slow and the water backs ups and spills onto the counter. The best cup of coffee is one where the water flows at a rate slow enough to absorb the most flavor from the beans, but fast enough that it passes through the filter without backing up. And this best cup of coffee occurs at what is known as the directed percolation transition.

This may not seem relevant to fluid turbulence, but in earlier work, the team and other researchers in the field had evidence that the directed percolation transition had the same statistical properties as laminar-turbulent transitions.

"This problem has been around for nearly 150 years and required a bit of unconventional thinking to solve," said Goldenfeld, who also holds appointments in the Jacobs School of Engineering and the Halicioğlu Data Science Institute. "And time. Some of the team members have been working on this aspect of the problem for well over a decade."

Indeed, in 2016, the Hof group studied the laminar-turbulent transition experimentally in a circular geometry, at the same time that Goldenfeld and collaborators developed their theory of the laminar-turbulent transition.

Although the Hof group had demonstrated directed percolation in a circular geometry, what happens in an open geometry like a pipe remained unclear. Moreover, the experiments are impractical to do in a pipe geometry. While a circle is never-ending, the researchers estimated that to perform the same experiment in a pipe would require a length of 2.5 miles, and it would take centuries to collect the necessary data points.

To make progress, the team did two things. First, they used pressure sensors to observe the puffs in a pipe, and measured precisely how the puffs influenced each other's motion. Inputting the data into a molecular dynamics computer simulation, they were able to show that statistically, near the laminar-turbulent transition, puff behavior was in excellent agreement with the directed percolation transition.

Second, they used statistical mechanics to mathematically predict the behavior of the puffs, using techniques from phase transition physics. This too validated the hypothesis of a directed percolation transition.

Through this research, the team also discovered something unexpected from both the detailed experiments and the statistical mechanical theory: like cars on the freeway in rush hour, puffs are prone to traffic jams. If a puff fills the width of a pipe, nothing can move past it, which means other puffs may build up behind it. And just as you might wonder why traffic jams occur and why they clear up with no identifiable cause, puff jams can also form and dissipate on their own, in a way that statistical mechanics describes. Puff jams tend to "melt" at the critical transition point from laminar to turbulent flow, giving way to the special statistical behavior of the directed percolation transition.

Goldenfeld commented: "This work not only closes one chapter on the laminar-turbulent transition in pipes, but shows how insights from different scientific disciplines can unexpectedly illuminate a difficult problem. Without a statistical mechanics perspective, understanding this quintessential fluid mechanics phenomenon would have been impossible."

This research was funded in part by the Simons Foundation (662985 and 662960) and the Ministry of Science and Technology, Taiwan (MOST 109-2112-M-001-017-MY3 and MOST 111-2112-M-001-027-MY3).

Full list of authors: Nigel Goldenfeld (UC San Diego), Björn Hof and Vasudevan Mukund (both Institute of Science and Technology Austria), Hong-Yan Shih (Institute of Physics, Academia Sinica (Taiwan)), Gaute Linga (the Njord Center, University of Oslo), Joachim Mathiesen (Niels Bohr Institute, University of Copenhagen), and Grégoire Lemoult (Université Le Havre Normandie).

Definitions

Laminar flow: a type of fluid flow where the fluid moves in smooth, orderly layers, with little to no mixing between them.

Directed percolation: a process where connections or flows occur in a specific direction, often used to model the spread of substances through a medium.

Non-equilibrium phase transition: a change in the state of a system that occurs when it is not in thermal equilibrium, often driven by external forces or energy input. These transitions occur in systems experiencing constant change, such as varying temperature, pressure or flow rates.

Puffs: regions of turbulence that can form and move within a flow, typically in a pipe or channel. They occur in the transitional phase between laminar and fully turbulent flows.

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Story Source:

Materials provided by University of California - San Diego . Original written by Michelle Franklin. Note: Content may be edited for style and length.

Journal Reference :

• Grégoire Lemoult, Vasudevan Mukund, Hong-Yan Shih, Gaute Linga, Joachim Mathiesen, Nigel Goldenfeld, Björn Hof. Directed percolation and puff jamming near the transition to pipe turbulence . Nature Physics , 2024; DOI: 10.1038/s41567-024-02513-0

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1000 Solved Problems in Modern Physics 2010th Edition

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• ISBN-10 3642043321
• ISBN-13 978-3642043321
• Edition 2010th
• Publisher Springer
• Publication date July 5, 2010
• Language English
• Dimensions 6.25 x 1.5 x 9 inches
• Print length 648 pages
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Editorial Reviews

From the reviews:

“The book provides a collection of problems and solutions in physics targeting mainly undergraduate students. … The book focuses mainly on basic problems in quantum mechanics, nuclear physics and particle physics. … the book could be a useful addition to problem and solution books in physics for undergraduate students.” (Willi-Hans Steeb, zbMATH, Vol. 1271, 2013)

From the Back Cover

This book basically caters to the needs of undergraduates and graduates physics students in the area of modern physics, specially particle and nuclear physics. Lecturers/tutors may use it as a resource book. The contents of the book are based on the syllabi currently used in the undergraduate courses in USA, U.K., and other countries. The book is divided into 10 chapters, each chapter beginning with a brief but adequate summary and necessary formulas, tables and line diagrams followed by a variety of typical problems useful for assignments and exams. Detailed solutions are provided at the end of each chapter.

About the Author

The author obtained his Doctoral degree from University of Bristol, U.K. under the supervision of Emeritus Professor Dr.D.H. Perkins, FRS. The author has worked in high-energy physics for a number of years using photographic emulsions exposed at CERN. He has also used low-energy facilities at Nuclear Science Center at New Delhi. He was a postdoctoral fellow at the University of Ottawa, visitor to CERN, visiting professor at the University of Tebrez. He has published 40 research papers in International Journals and gave lectures on Nuclear physics, particle physics, quantum mechanics, classical mechanics, mathematical physics, atomic and molecular physics and relativity at undergraduate and graduate levels at various universities for several years. He was a Professor and Head of the Department of Physics and Chairman, Board of studies at the Osmania University.

Product details

• Publisher ‏ : ‎ Springer; 2010th edition (July 5, 2010)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 648 pages
• ISBN-10 ‏ : ‎ 3642043321
• ISBN-13 ‏ : ‎ 978-3642043321
• Item Weight ‏ : ‎ 2.75 pounds
• Dimensions ‏ : ‎ 6.25 x 1.5 x 9 inches
• #648 in Atomic & Nuclear Physics
• #935 in Molecular Physics (Books)
• #1,005 in Particle Physics

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Ahmad a. kamal.

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