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The Quantum Cookbook: Mathematical Recipes of the Foundations for Quantum Mechanics
Quantum mechanics is an extraordinarily successful scientific theory. But it is also completely mad. Although the theory quite obviously works, it leaves us chasing ghosts and phantoms; particles that are waves and waves that are particles; cats that are at once both alive and dead; lots of seemingly spooky goings-on; and a desperate desire to lie down quietly in a darkened room. The Quantum Cookbook explains why this is. It provides a unique bridge between popular exposition and formal textbook presentation, written for curious readers with some background in physics and sufficient mathematical capability. It aims not to teach readers how to do quantum mechanics but rather helps them to understand how to think about quantum mechanics. Each derivation is presented as a 'recipe' with listed ingredients, including standard results from the mathematician's toolkit, set out in a series of easy-to-follow steps. The recipes have been written sympathetically, for readers who - like the
author - will often struggle to follow the logic of a derivation which misses out steps that are 'obvious', or which use techniques that readers are assumed to know.
author - will often struggle to follow the logic of a derivation which misses out steps that are 'obvious', or which use techniques that readers are assumed to know.
320 pages, Hardcover
First published March 10, 2020
6 people are currently reading
91 people want to read
About the author
Jim Baggott
23 books146 followersJim Baggott completed his doctorate in physical chemistry at the University of Oxford and his postgraduate research at Stanford University.
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Displaying 1 - 5 of 5 reviews
September 6, 2021
“For curious readers with some background in physics and sufficient mathematical capability, neither popular exposition nor textbook provides them with what they need.”
The first nine chapters of The Quantum Cookbook are each dedicated to a foundational principle of quantum mechanics, starting with Planck’s derivation of the Planck-Einstein relation and ending with Dirac’s derivation of the relativistic wave equation. Each chapter starts with a historical background, which helps the reader better understand the reasoning of physicists at the time, and then moves on to introduce the necessary physical concepts, before the mathematical derivation. Baggott addresses each mathematical derivation with a list of “ingredients” and “recipes”, and I found this method to be an excellent addition, giving us readers a better idea of the “tools” that will be used, as well as the required steps.
“We reach for Born’s interpretation and we deduce that the probability of finding the electron is similarly extended and delocalized - it has a certain probability of being found ‘here’, ‘there’, and, well, anywhere it has non-zero amplitude. Yet we anticipate that it will register on a photographic plate or in a detector as a single, self-contained particle that is unambiguously ‘here’, and nowhere else.”
The last three chapters are dedicated to quantum formalism and quantum mechanics philosophical questions, from the problem of quantum measurement and ‘collapse of the wavefunction’, to entanglement and quantum non-locality. Is the wavefunction real? Is there really such thing as a physical collapse? Is the registering of the measurement outcome just an update of the observer’s state of knowledge about it? As Baggott wrote, “The debate continues. After a thirty-year personal journey in search of the meaning of quantum mechanics, I can happily attest to the fact I still don’t understand it. But I think I now understand why.”
The closing chapters of this book were very good and felt like the end of a great journey through quantum mechanics. I do have a few minor concerns though. Namely, the text could have been more clear at times and I think the different quantum numbers could have been presented in a more “digestible” way, as sometimes I had to go back a few pages to read again their descriptions.
Popular science books usually focus too much on the historical storytelling of quantum mechanics. On the other hand, formal textbooks often highlight in excess the mathematically abstract parts of quantum mechanics. Jim Baggott combined these two approaches and wrote an excellent book, which will be a great addition to that rare group of books that sit somewhere between a popular science book and a formal textbook.
The first nine chapters of The Quantum Cookbook are each dedicated to a foundational principle of quantum mechanics, starting with Planck’s derivation of the Planck-Einstein relation and ending with Dirac’s derivation of the relativistic wave equation. Each chapter starts with a historical background, which helps the reader better understand the reasoning of physicists at the time, and then moves on to introduce the necessary physical concepts, before the mathematical derivation. Baggott addresses each mathematical derivation with a list of “ingredients” and “recipes”, and I found this method to be an excellent addition, giving us readers a better idea of the “tools” that will be used, as well as the required steps.
“We reach for Born’s interpretation and we deduce that the probability of finding the electron is similarly extended and delocalized - it has a certain probability of being found ‘here’, ‘there’, and, well, anywhere it has non-zero amplitude. Yet we anticipate that it will register on a photographic plate or in a detector as a single, self-contained particle that is unambiguously ‘here’, and nowhere else.”
The last three chapters are dedicated to quantum formalism and quantum mechanics philosophical questions, from the problem of quantum measurement and ‘collapse of the wavefunction’, to entanglement and quantum non-locality. Is the wavefunction real? Is there really such thing as a physical collapse? Is the registering of the measurement outcome just an update of the observer’s state of knowledge about it? As Baggott wrote, “The debate continues. After a thirty-year personal journey in search of the meaning of quantum mechanics, I can happily attest to the fact I still don’t understand it. But I think I now understand why.”
The closing chapters of this book were very good and felt like the end of a great journey through quantum mechanics. I do have a few minor concerns though. Namely, the text could have been more clear at times and I think the different quantum numbers could have been presented in a more “digestible” way, as sometimes I had to go back a few pages to read again their descriptions.
Popular science books usually focus too much on the historical storytelling of quantum mechanics. On the other hand, formal textbooks often highlight in excess the mathematically abstract parts of quantum mechanics. Jim Baggott combined these two approaches and wrote an excellent book, which will be a great addition to that rare group of books that sit somewhere between a popular science book and a formal textbook.
April 22, 2024
Outstanding.
For anyone with decent maths (e.g. university entry level, I guess) – basic differential calculus, basic vector calculus (e.g. grad, Laplacian), good algebra (i.e. equation munging) – and some physics, this is by far the best introductory book to quantum theory I've read. It's also a delightful and entertaining read. The chapter on Dirac's derivation of the relativistic wave equation is astonishing – even if you know the QED punchline. I also liked how the prologue put classical physics in context and introduced the Hamiltonian.
Baggott dedicates the book: To myself, aged 18, when I took my first class in quantum mechanics. And he's nailed it. I would have given my right arm for this book when I began to teach myself quantum theory – albeit armed with a maths degree, which is a enormous help with this topic.
Not a gripe, more a suggestion: Baggott, quite rightly, doesn't derive Maxwell's equations and instead points to Melia's, Electrodynamics. I think Griffiths's, Introduction to Electrodynamics, is more appropriate at this (and my) level.
For anyone with decent maths (e.g. university entry level, I guess) – basic differential calculus, basic vector calculus (e.g. grad, Laplacian), good algebra (i.e. equation munging) – and some physics, this is by far the best introductory book to quantum theory I've read. It's also a delightful and entertaining read. The chapter on Dirac's derivation of the relativistic wave equation is astonishing – even if you know the QED punchline. I also liked how the prologue put classical physics in context and introduced the Hamiltonian.
Baggott dedicates the book: To myself, aged 18, when I took my first class in quantum mechanics. And he's nailed it. I would have given my right arm for this book when I began to teach myself quantum theory – albeit armed with a maths degree, which is a enormous help with this topic.
Not a gripe, more a suggestion: Baggott, quite rightly, doesn't derive Maxwell's equations and instead points to Melia's, Electrodynamics. I think Griffiths's, Introduction to Electrodynamics, is more appropriate at this (and my) level.
December 24, 2020
This book presents “mathematical recipes for the foundation of Quantum Mechanics”. Each recipe is a self-contained treatment of a specific building block of this foundation, where the recipe is clearly structured by providing the historical background and context of the building block, followed by the list of “ingredients” needed for the recipe, the list of steps of the actual recipe and then the detailed presentation of each of these steps. These detailed steps involve mathematics which from time to time are quite advanced.
Author Jim Bagott does a great job in many aspects. Presenting the building blocks as structured recipes helps the reader understanding these topics by reading between and looking through the lines of the mathematical derivations. Outlining the historical background helps the reader understanding the line of thinking and reasoning of famous scientists like Einstein, Heisenberg, Schrödinger, Pauli, Dirac, Bohr, Born, who worked on these building blocks trying to build, by “trial and error”, a consistent foundation of Quantum Mechanics.
Bagott took care to present the recipes in a specific order, which helps to gain practical “cooking experience”, starting with the more basic recipes, but which also helps to better understand the (on-going) strong discussions and opposite opinions on topics like quantum measurement, entanglement and quantum non-locality.
To give you an impression of these recipes, Bagott starts explaining the quantization of blackbody radiation, leading to the concept of photons, then explaining the wave-behavior of electrons, leading to quantum numbers and quantum jumps. A next recipe explains this wave-particle duality in more details emphasizing the interpretation problems coming with it (how to know where to jump to..?). More advanced recipes follow, on topics like quantum probability, the uncertainty principle, the Pauli exclusion principle, the relativistic wave equation, and main “courses” on quantum measurement, entanglement and quantum non-locality.
Personally I learned a lot from this book. Most of these building blocks, were not new to me, but the way they were presented and given their context, helped me to gain new or at least better insights, especially the link with relativity and the work of Einstein on these topics were clarifying.
After reading the book twice, I’m left with wonder: the incredible precision provided by mathematics in explaining results of actual experiments seems to conflict with the “lack” of basic understanding of the quantum world, where this lack is even more emphasized by the discussion on how to “look” at this quantum world, either as a classical world view with additional “quantum” rules imposed, or as a totally new non-visualizable technical and mechanical view on reality.
Masterchef Jim Bagott serves an excellent way to getter a better taste for our quantum reality, but as always “the proof of the pudding is in the eating”, each recipe providing handles to gain a better understanding, bite by bite...
Author Jim Bagott does a great job in many aspects. Presenting the building blocks as structured recipes helps the reader understanding these topics by reading between and looking through the lines of the mathematical derivations. Outlining the historical background helps the reader understanding the line of thinking and reasoning of famous scientists like Einstein, Heisenberg, Schrödinger, Pauli, Dirac, Bohr, Born, who worked on these building blocks trying to build, by “trial and error”, a consistent foundation of Quantum Mechanics.
Bagott took care to present the recipes in a specific order, which helps to gain practical “cooking experience”, starting with the more basic recipes, but which also helps to better understand the (on-going) strong discussions and opposite opinions on topics like quantum measurement, entanglement and quantum non-locality.
To give you an impression of these recipes, Bagott starts explaining the quantization of blackbody radiation, leading to the concept of photons, then explaining the wave-behavior of electrons, leading to quantum numbers and quantum jumps. A next recipe explains this wave-particle duality in more details emphasizing the interpretation problems coming with it (how to know where to jump to..?). More advanced recipes follow, on topics like quantum probability, the uncertainty principle, the Pauli exclusion principle, the relativistic wave equation, and main “courses” on quantum measurement, entanglement and quantum non-locality.
Personally I learned a lot from this book. Most of these building blocks, were not new to me, but the way they were presented and given their context, helped me to gain new or at least better insights, especially the link with relativity and the work of Einstein on these topics were clarifying.
After reading the book twice, I’m left with wonder: the incredible precision provided by mathematics in explaining results of actual experiments seems to conflict with the “lack” of basic understanding of the quantum world, where this lack is even more emphasized by the discussion on how to “look” at this quantum world, either as a classical world view with additional “quantum” rules imposed, or as a totally new non-visualizable technical and mechanical view on reality.
Masterchef Jim Bagott serves an excellent way to getter a better taste for our quantum reality, but as always “the proof of the pudding is in the eating”, each recipe providing handles to gain a better understanding, bite by bite...
July 23, 2024
This book is the first one I read about quantum mechanics which assembly in a very readable way, the history, the mathematics and the philosophical discussions around it. I think Baggott achieves a level for general public information (skipping the equations and focusing only in the explanation), if you want to go deeper and have some math background, you can also follow the details in the equations and get their interpretation and, if you want to go with an extra effort, you can also can follow the recommendations and bibliography in every chapter.
The journey through the book is amazing through the most important milestones in the development of quantum mechanics. If you do like this topics without being a physicist and have some math background, this book definitely worth the reading.
The journey through the book is amazing through the most important milestones in the development of quantum mechanics. If you do like this topics without being a physicist and have some math background, this book definitely worth the reading.
Currently reading
October 3, 2022This book contains a lot Calculus and Advanced theoretical physics. It is very thorough to explain the major derivation of mathematical equation of Quantum Mechanics. Perhaps when I get re-acquainted with Calculus I will revisit this book.
Displaying 1 - 5 of 5 reviews