physics 3000 solved problems

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3,000 Solved Problems in Physics (Schaum's Solved Problems Series) Paperback – 16 May 1990

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It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams!

Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's!

If you don't have a lot of time but want to excel in class, use this book to:

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Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams.

Inside you will find:

• 3000 solved problems with complete solutions--the largest selection of solved problems yet published on this subject
• An index to help you quickly locate the types of problems you want to solve
• Problems like those you'll find on your exams
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If you want top grades and thorough understanding of physics, this powerful study tool is the best tutor you can have!

• ISBN-10 0070257345
• ISBN-13 978-0070257344
• Publisher McGraw-Hill Education
• Publication date 16 May 1990
• Language English
• Dimensions 20.96 x 3.18 x 27.31 cm
• Print length 792 pages
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• Publisher ‏ : ‎ McGraw-Hill Education (16 May 1990)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 792 pages
• ISBN-10 ‏ : ‎ 0070257345
• ISBN-13 ‏ : ‎ 978-0070257344
• Dimensions ‏ : ‎ 20.96 x 3.18 x 27.31 cm
• 5,356 in Higher Mathematical Education
• 9,668 in Popular Science Physics

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3000 Solved Problems in Physics (Schaum Outline Series) Paperback – 1 July 2017

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3,000 solved problems in physics

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• Mathematical introduction
• Equilibrium of concurrent forces
• Kinematics in one dimension
• Newton's laws of motion
• Motion in a plane I
• Motion in a plane II
• Work and energy
• Power and simple machines
• Impulse and momentum
• Statics of rigid bodies
• Rotational motion I: kinematics and dynamics
• Rotational motion II: kinetic energy, angular impulse, angular momentum
• Matter in bulk
• Simple harmonic motion
• Hydrostatics
• Hydrodynamics
• Temperature and thermal expansion
• Heat and calorimetry
• Heat transfer
• Gas laws and kinetic theory
• The first law of thermodynamics
• The second law of thermodynamics
• Wave motion
• Coulomb's law and electric fields
• Electric potential and capacitance
• Simple electric circuits
• The magnetic field
• Magnetic properties of matter
• Induced EMF: generators and motors
• Electric circuits
• Electromagnetic waves
• Light and optical phenomena
• Mirrors, lenses, and optical instruments
• Interference, diffraction, and polarization
• Special relativity
• Particles of light and waves of matter
• Modern physics: atoms, nuclei, solid-state electronics.

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• Schaums 3000 Solved Problems i...

Schaums 3000 Solved Problems in Physics Revised.

• Description
• Table of Contents

Similar Items

• Mathematical introduction
• Equilibrium of concurrent forces
• Kinematics in one dimension
• Newton's laws of motion
• Motion in a plane I
• Motion in a plane II
• Work and energy
• Power and simple machines
• Impulse and momentum
• Statics of rigid bodies
• Rotational motion I : kinematics and dynamics
• Rotational motion II : kinetic energy, angular impulse, angular momentum
• Matter in bulk
• Simple harmonic motion
• Hydrostatics
• Hydrodynamics
• Temperature and thermal expansion
• Heat and calorimetry
• Heat transfer
• Gas laws and kinetic theory
• The first law of thermodynamics
• The second law of thermodynamics
• Wave motion
• Coulomb's law and electric fields
• Electric potential and capacitance
• Simple electric circuits
• The magnetic field
• Magnetic properties of matter
• Induced EMF : generators and motors
• Electric circuits
• Electromagnetic waves
• Light and optical phenomena
• Mirrors, lenses, and optical instruments
• Interference, diffraction, and polarization
• Special relativity
• Particles of light and waves of matter
• Modern physics : atoms, nuclei, solid-state electronics.
• Feynman's tips on physics : reflections, advice, insights, practice : a problem-solving supplement to the Feynman lectures on physics / by: Feynman, Richard P. (Richard Phillips), 1918-1988 Published: (2013)
• Methods for solving mathematical physics problems by: Agoshokov, V. I. Published: (2006)
• 1000 solved problems in classical physics : an exercise book / by: Kamal, Ahmad A. Published: (2011)
• 1000 solved problems in classical physics an exercise book / by: Kamal, Ahmad A. Published: (2011)
• Schaum's outline of theory and problems of advanced mathematics for engineers and scientists, by: Spiegel, Murray R. Published: (1971)

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Scientists use generative AI to answer complex questions in physics

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When water freezes, it transitions from a liquid phase to a solid phase, resulting in a drastic change in properties like density and volume. Phase transitions in water are so common most of us probably don’t even think about them, but phase transitions in novel materials or complex physical systems are an important area of study.

To fully understand these systems, scientists must be able to recognize phases and detect the transitions between. But how to quantify phase changes in an unknown system is often unclear, especially when data are scarce.

Researchers from MIT and the University of Basel in Switzerland applied generative artificial intelligence models to this problem, developing a new machine-learning framework that can automatically map out phase diagrams for novel physical systems.

Their physics-informed machine-learning approach is more efficient than laborious, manual techniques which rely on theoretical expertise. Importantly, because their approach leverages generative models, it does not require huge, labeled training datasets used in other machine-learning techniques.

Such a framework could help scientists investigate the thermodynamic properties of novel materials or detect entanglement in quantum systems, for instance. Ultimately, this technique could make it possible for scientists to discover unknown phases of matter autonomously.

“If you have a new system with fully unknown properties, how would you choose which observable quantity to study? The hope, at least with data-driven tools, is that you could scan large new systems in an automated way, and it will point you to important changes in the system. This might be a tool in the pipeline of automated scientific discovery of new, exotic properties of phases,” says Frank Schäfer, a postdoc in the Julia Lab in the Computer Science and Artificial Intelligence Laboratory (CSAIL) and co-author of a paper on this approach.

Joining Schäfer on the paper are first author Julian Arnold, a graduate student at the University of Basel; Alan Edelman, applied mathematics professor in the Department of Mathematics and leader of the Julia Lab; and senior author Christoph Bruder, professor in the Department of Physics at the University of Basel. The research is published today in Physical Review Letters.

Detecting phase transitions using AI

While water transitioning to ice might be among the most obvious examples of a phase change, more exotic phase changes, like when a material transitions from being a normal conductor to a superconductor, are of keen interest to scientists.

These transitions can be detected by identifying an “order parameter,” a quantity that is important and expected to change. For instance, water freezes and transitions to a solid phase (ice) when its temperature drops below 0 degrees Celsius. In this case, an appropriate order parameter could be defined in terms of the proportion of water molecules that are part of the crystalline lattice versus those that remain in a disordered state.

In the past, researchers have relied on physics expertise to build phase diagrams manually, drawing on theoretical understanding to know which order parameters are important. Not only is this tedious for complex systems, and perhaps impossible for unknown systems with new behaviors, but it also introduces human bias into the solution.

More recently, researchers have begun using machine learning to build discriminative classifiers that can solve this task by learning to classify a measurement statistic as coming from a particular phase of the physical system, the same way such models classify an image as a cat or dog.

The MIT researchers demonstrated how generative models can be used to solve this classification task much more efficiently, and in a physics-informed manner.

The Julia Programming Language , a popular language for scientific computing that is also used in MIT’s introductory linear algebra classes, offers many tools that make it invaluable for constructing such generative models, Schäfer adds.

Generative models, like those that underlie ChatGPT and Dall-E, typically work by estimating the probability distribution of some data, which they use to generate new data points that fit the distribution (such as new cat images that are similar to existing cat images).

However, when simulations of a physical system using tried-and-true scientific techniques are available, researchers get a model of its probability distribution for free. This distribution describes the measurement statistics of the physical system.

A more knowledgeable model

The MIT team’s insight is that this probability distribution also defines a generative model upon which a classifier can be constructed. They plug the generative model into standard statistical formulas to directly construct a classifier instead of learning it from samples, as was done with discriminative approaches.

“This is a really nice way of incorporating something you know about your physical system deep inside your machine-learning scheme. It goes far beyond just performing feature engineering on your data samples or simple inductive biases,” Schäfer says.

This generative classifier can determine what phase the system is in given some parameter, like temperature or pressure. And because the researchers directly approximate the probability distributions underlying measurements from the physical system, the classifier has system knowledge.

This enables their method to perform better than other machine-learning techniques. And because it can work automatically without the need for extensive training, their approach significantly enhances the computational efficiency of identifying phase transitions.

At the end of the day, similar to how one might ask ChatGPT to solve a math problem, the researchers can ask the generative classifier questions like “does this sample belong to phase I or phase II?” or “was this sample generated at high temperature or low temperature?”

Scientists could also use this approach to solve different binary classification tasks in physical systems, possibly to detect entanglement in quantum systems (Is the state entangled or not?) or determine whether theory A or B is best suited to solve a particular problem. They could also use this approach to better understand and improve large language models like ChatGPT by identifying how certain parameters should be tuned so the chatbot gives the best outputs.

In the future, the researchers also want to study theoretical guarantees regarding how many measurements they would need to effectively detect phase transitions and estimate the amount of computation that would require.

This work was funded, in part, by the Swiss National Science Foundation, the MIT-Switzerland Lockheed Martin Seed Fund, and MIT International Science and Technology Initiatives.

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Researchers at MIT and elsewhere have developed a new machine-learning model capable of “predicting a physical system’s phase or state,” report Kyle Wiggers and Devin Coldewey for TechCrunch . 

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Related Links

• Frank Schäfer
• Alan Edelman
• Computer Science and Artificial Intelligence Laboratory
• Department of Mathematics
• Department of Electrical Engineering and Computer Science

Related Topics

• Mathematics
• Computer science and technology
• Artificial intelligence
• Computer modeling
• Computer Science and Artificial Intelligence Laboratory (CSAIL)
• Electrical Engineering & Computer Science (eecs)

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3000 solved problems in physics

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• Quantum Research

Quantum working groups push for near-term use cases

Algorithm discovery is what will take us from quantum utility to advantage. let’s undertake that discovery as a community, with both use case subject matter experts and quantum researchers collaborating to discover where quantum has the potential to offer a benefit..

22 May 2024

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IBM Quantum Working Groups: healthcare & life sciences, materials science, high energy physics, optimization, and sustainability.

In the past two years, IBM and collaborators launched five working groups to spur quantum algorithmic development in domains with promising potential for quantum benefits: healthcare & life sciences, materials science, high energy physics, optimization, and sustainability. Each of these groups meet regularly to figure out problems of interest, what makes them difficult, what is state-of-the-art, what are potential first use cases and where quantum can provide benefit in the near term and in the future.

With the kickoff of the sustainability quantum working group this month, all of our groups are now up and running, guiding their respective fields toward quantum advantage. The groups are now releasing white papers and forming active research collaborations researching what quantum might bring to each respective group — including open problems with the potential for a quantum speedup.

Why are these working groups necessary? We’ve always said that quantum advantage requires two things: The first is demonstrating that quantum hardware is capable of running quantum circuits that can’t be exactly simulated by classical computers. We call this part quantum utility, and the first evidence of utility was demonstrated in a paper featured on the cover of Nature last year. The second is demonstrating that those quantum circuits are actually the best way to solve the problem, over any other state-of-the-art method.

Read about the paper from IBM and UC Berkeley that showed a path toward useful quantum computing

Realizing and delivering quantum advantage requires the help of the broader quantum community. Subject matter experts must figure out the open and important problems in their field, then figure out which of those problems necessarily can not be solved using existing classical methods. Together with quantum expertise, they can determine which subset of those problems is good for attempting a quantum solution. Finally, they must map the problems to a quantum computer and then run those problems on ever-maturing quantum hardware, comparing those results to existing classical methods. We believe this exploration will be crucial to realizing quantum advantage in the near term.

Now that each group is up and running, we’re ready to talk about who these working groups are and how they’re working to bring quantum advantage to their respective domain.

High-energy physics

All across the world, laboratories are studying matter at its fundamental level — colliding beams of particles to perform high-energy experiments, which can lead to the discovery of new particles to fill in the gaps in our understanding of physics. But these experiments generate an immense amount of data — and require an exponentially increasing amount of computing power to handle. For decades, merely attempting to handle and analyze this data while collaborating across the world has led to major computing breakthroughs that impact how we use the internet today — CERN is responsible for the world wide web and maturing grid computing, for example.

The challenge of understanding the outputs of these experiments only grows as new more powerful experiments come online. Quantum computing has the potential to provide value here, especially since these experiments often deal with fundamentally quantum information. And so, in November of 2022, the Quantum Computing for High-Energy Physics (QC4HEP) Working Group gathered for the first time at CERN in Geneva. The working group included experts from CERN, DESY, Oak Ridge National Laboratory, the University of Tokyo, and research institutions around the world interested in how quantum computing could change the field.

In their 2023 white paper , 1 the QC4HEP group sought to list the use cases relevant to HEP with the goal of eventually running some of them on a utility-scale quantum processor. They concluded that quantum had the potential to impact HEP in two core areas: algorithms and methods for modeling high-energy physics problems, and numerical methods for analyzing experimental results, simulating the detectors used in the experiments, and simulating the events generated by colliding particles.

But HEP is uniquely positioned for another reason: these systems, too, follow the rules of quantum mechanics. Therefore, HEP may benefit from quantum computing on the shorter term, especially when it comes to simulating the dynamics of the systems they’re studying. We are dealing with systems that are very much quantum in nature — so using a quantum computer to solve these classes of problems makes a certain intuitive sense.

Furthermore, perhaps physicists will be able to combine information from quantum sensing in experiments and study it with quantum computers — analyzing quantum data with quantum resources.

Quantum computing shares an intimate link with high-energy physics, given that they operate on the same scale and follow the same basic set of rules. So we feel confident in saying that quantum has immense potential to accelerate the field of HEP.

Materials science

Many materials science problems are innately quantum, and quantum speedups in this field have the potential to benefit areas from our fundamental understanding of matter to industrial problems in energy storage, solar power, and more.

Today, materials science already incorporates a lot of high performance computing resources in order to run models for materials. However, exact simulations grow exponentially with the size of the system they’re trying to simulate. Materials scientists incorporate approximations to overcome this issue, but these approximations can either break down due to complexity of the material, or their simulation becomes too resource intensive.

That’s where quantum computing steps in. Some quantum algorithms promise exponential speedups or reduction in memory usage. And we already expect that quantum computing will be embedded into a classical supercomputing workflow as part of a broader vision for quantum-centric supercomputing. Therefore, materials science is poised to begin incorporating quantum resources without making big changes to existing workflows.

The Materials Science Working Group kicked off in March of 2023 at the University of Chicago, including members from Oak Ridge National Lab, RIKEN, the University of Chicago, Boeing, Bosch, and ExxonMobil. After presentations on pertinent topics, breakout sessions, and follow-ups to begin research, the group published their white paper 2 in December, 2023.

Those algorithms lend themselves to several relevant use cases. Perhaps the most popular is the simulation of a system’s ground state — a key to understanding how the material will behave during chemical reactions. The paper goes on to list further uses in simulation, calculating excited states, vibrational structure calculations, and more.

Healthcare and life sciences

And if quantum has the potential for impacts at the chemistry level, why not a step higher, at the biology level? While benefits might be further off on the horizon for these more complex systems like cells and proteins, there would be immense potential to benefit humanity as a whole. That’s the rationale behind the Healthcare and Life Sciences (HCLS) Working Group.

After all, groundbreaking technological developments have already started transforming HCLS — new microscopy techniques allow more detailed looks than ever before into the human body, while new methods allow biologists to create 3D maps of tissues at the cellular level, for example. This has led to enormous international efforts, from creating a cell atlas to creating lifesaving vaccines to mapping the human genome, and has even changed the way we go about curing disease. Perhaps there are previously incurable diseases — aggressive cancers, for example — for which technological advancement could provide a solution in the future.

The HCLS working group kicked off in April, 2023 at Cleveland Clinic, featuring members from the non-profit academic medical center, University of Chicago, Moderna, Harvard, and elsewhere. In their white paper , 3 the working group members presented a vision to reimagine healthcare and drug discovery called “Quantum Enabled Cell-Centric Therapeutics.” By combining HPC with quantum algorithms, they hope to understand the behaviors of cells in diseased tissue at the individual level, with the hope of eventually creating better treatments.

Quantum Enabled Cell-Centric Therapeutics covers four key areas:

• First is the use of quantum neural networks (QNNs) to learn about how immune cells send and receive signals from limited data.
• The second is using hybrid classical-quantum generative neural networks to model the environment around tumors.
• The third is using a novel hybrid quantum optimization algorithm to model an individual cells’ response to a therapeutic intervention.
• And the fourth is using quantum to perform topological data analysis to better capture the interactions between cells.

We don’t expect quantum to transform HCLS tomorrow — but this work serves as a call to action to begin exposing the broader community to the potential of incorporating quantum algorithms into HCLS research. Quantum is already starting to address problems for certain fields where there’s the potential for competition with classical methods, or even advantage. For HCLS, the time is now to start thinking about extracting utility so we can make positive impacts sooner.

Optimization

Last but not least, we have our working group devoted to problems that interest stakeholders across domains: optimization. If we were to find a quantum advantage for an optimization problem, it would potentially yield much business value — so there’s lots of interest in the field. And there is hope that maybe one day, quantum could provide speedups, find cheaper solutions, higher-quality solutions, or different kinds of solutions.

The Optimization Working Group, featuring partners such as energy company E.ON and financial services company Wells Fargo, released their own white paper 4 in December of 2023, too. The paper begins by setting the expectation that we’re still working to figure out how optimization will benefit from quantum. For example, the famous Grover’s search algorithm offers only a quadratic speedup over classical methods, and recent work has found that the overhead for running the algorithm with error mitigation might wash out any potential gains.

But we should not only be looking for algorithms with mathematical proofs of some speedup since this isn’t required when seeking practical quantum advantages. For example, we consider a group of problems called NP-intermediate problems where it’s not clear if they can be efficiently solved on a classical computer (P) or grouped with the hardest problems for which we can efficiently check whether an answer is correct (NP-complete). Factoring numbers is in this complexity class, and Shor’s algorithm provides an exponential speedup over the best-known methods. Furthermore, for some problems — like those in the NP-complete class — approximate solutions can be nearly as valuable.

That being said, there are plenty of quantum optimization algorithms with potential to provide value — the quantum approximate optimization algorithm , the quantum adiabatic algorithm , Gibbs sampling , and more. To understand the potential of these algorithms, we have to systematically benchmark them on difficult problems and compare the result to the state of the art. While benchmarking problems can be artificial, we also need to identify practically relevant optimization problems that are really hard classically. Both will guide our research towards a quantum advantage in optimization.

Today, working group members are already using applications like financial asset allocation or the transition to sustainable energy as a playground to derive real-world-inspired benchmarking problems. They hope to continue this effort as we continue our exploration into quantum for optimization.

What’s next: sustainability

Just this month, another group kicked off with PINQ², Université de Sherbrooke, Hydro-Québec, University of Luxembourg, and E.ON. The objective of this Working Group is to gather the best scientists from the quantum and sustainability communities with the ambitious goal of designing quantum computing and hybrid solutions to address sustainability challenges in the fields of materials and energy. The unique format of the kickoff workshop paved the way towards bridging the gaps between the quantum community and sustainability domain experts.

After the kickoff, the group left with five focus areas covering topics across sustainable materials and optimization. Together, they hope the advances from this collaboration could help us store and deliver energy more efficiently, improve our power systems, and tackle climate change overall.

We expect the collaborations and insights generated from the working groups to generate scientific advances across domains. But we hope that, even more than new research, they will demonstrate a path to quantum advantage on today’s utility-scale systems.

Di Meglio, A., Jansen, K., Tavernelli, I., et al. Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group. arXiv. https://arxiv.org/abs/2307.03236

Alexeev, Y., Amsler, M., Baity, P., et al. Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions. arXiv. https://arxiv.org/abs/2312.09733

Basu, S., Born, J., Bose, A., et al. Towards quantum-enabled cell-centric therapeutics. arXiv. https://arxiv.org/abs/2307.05734

Abbas, A., Ambainis, A., Augustino, B., et al. Quantum Optimization: Potential, Challenges, and the Path Forward. arXiv. https://arxiv.org/abs/2312.02279

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