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Quantum Mechanics and Path Integrals
quantum mechanics, shrodinger description, measurements and operators, perturbation method, transition elements, harmonic oscillators, QED, statistical mechainics, the variational method, other probability problems
365 pages, Hardcover
Published June 1, 1965
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1,051 people want to read
About the author
Richard P. Feynman
238books6,470followersRichard Phillips Feynman was an American physicist known for the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as work in particle physics (he proposed the parton model). For his contributions to the development of quantum electrodynamics, Feynman was a joint recipient of the Nobel Prize in Physics in 1965, together with Julian Schwinger and Sin-Itiro Tomonaga. Feynman developed a widely used pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime and after his death, Feynman became one of the most publicly known scientists in the world.
He assisted in the development of the atomic bomb and was a member of the panel that investigated the Space Shuttle Challenger disaster. In addition to his work in theoretical physics, Feynman has been credited with pioneering the field of quantum computing, and introducing the concept of nanotechnology (creation of devices at the molecular scale). He held the Richard Chace Tolman professorship in theoretical physics at Caltech.
-wikipedia
See Ричард Фейнман
He assisted in the development of the atomic bomb and was a member of the panel that investigated the Space Shuttle Challenger disaster. In addition to his work in theoretical physics, Feynman has been credited with pioneering the field of quantum computing, and introducing the concept of nanotechnology (creation of devices at the molecular scale). He held the Richard Chace Tolman professorship in theoretical physics at Caltech.
-wikipedia
See Ричард Фейнман
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Displaying 1 - 12 of 12 reviews
June 22, 2017
There is a funny piece of trivia associated with the book's co-author, Albert Hibbs: he once appeared as a contestant on Groucho Marx's You Bet Your Life. When I was in graduate school You Bet Your Life was re-broadcast by a local station late the evening about the time I got home from school and my roommate and I had made a ritual of watching it. I was totally shocked and delighted to see Prof. Hibbs one evening, out of the blue, just like that. At the time I felt kind of proud (or perhaps just inflated!) because I was perhaps the one-in-a-thousand who knew who he was and his connection to path integrals and the great Feynman who, in those days, still was not widely known outside the physical sciences--this being several years before the Challenger disaster which brought him into public view; pitiably just before his untimely death.
I don't know how this happened but it doesn't seem to be unrelated to the special nature of this book and the life of that titan of physics, Richard Feynman. As is well known, Feynman was a colorful character--what we used to call "a character"--and it wouldn't surprise me if he put Dr. Hibbs up to it.
I can no longer review this book in a technical sense; having moved on from physics almost 30 years ago. But I can give a flavor of what it was like to read it. To appreciate its thrill one must recall that in those days, the classical interpretation of quantum mechanics was very much in sway. It was strictly probabilistic and students were told there was no point in trying to imagine some underlying process governing the probabilities. Case closed. Sure there were individual physicists--some of great repute--who viewed quantum theory from novel angles. Alfred Lande was one, David Bohm another and even Dirac had proffered some interesting musing in his classic textbook on the subject. There was the quirky and famous EPR paper which put forth its (in)famous paradox; but most workers had little time for what seemed a speculative matter best left to those who had achieved the leisure and reputation to worry about it. It was a time when people, like Roger Penrose, with their lively interpretations of the wavefunction and their subsequent influence were still in the future.
Along comes (to me) Richard Feynman who, in 1948, wrote this totally wacky paper which, as I recall, began with the question of how one could integrate with respect to an infinite number of variables. For me, its immediate appeal came, not from its physics, but from the fact that Feynman had appeared to pose a genuine problem in the theory of the integral--something that I was very much infatuated with at the time. I too had wondered about this but lacked the technical skill and imagination to bring it beyond mere "bathtub cogitation." So I was very eager to know how this could be done. I had grasped the magnificent Lebesgue theory for finite dimensional spaces; how it gave meaning to the integration of functions "too pathological" for the Riemann approach. Was it possible that Feynman had delivered us an integral for infinite dimensional spaces too? Would it too shed light on even weirder functions--functions that had an infinite number of variables?...
In a sense the answer was that it did, though it had been provided decades before Feynman’s own work. Nor did he probably understand the technical difficulties involved from a measure theoretic perspective. In fact, it was Norbert Weiner who first broke ground in this area by formulating what is now called the Weiner measure. The Weiner process and its associated measure, partly intended as a mathematical representation of Brownian motion, gave rise to truly weird functions indeed. They were continuous everywhere while at the same time being differentiable nowhere. How much more pathologic can one get! It takes some thought to imagine such functions, unlike ordinary functions, because they consist of realizations which look somewhat like ordinary functions when graphed until one understands the fact that another graph of the same function will look completely different because it is a different realization. Another bizarre property is today called self-similarity in much the same sense as fractals. There are a host of other bizarre properties of such functions which, because of their technical nature, I won’t mention here.
I mentioned that Feynman probably did not fully understand the subtle nature of his mathematical invention. Unlike the Weiner measure, the measure associated with “Feynman’s process� can be considered a complex measure—sort of. I once took a class in stochastic integration from the renowned Monroe Donsker. After several class periods laying the ground work for the Weiner process and, in fact, deriving the Feynman-Kac formula (a beautiful formula!) which looks very much like a path-integral, I realized the relation between the two was that the latter can be transformed into the former via an imaginary time transformation—just as the Schrödinger equation becomes a diffusion equation, which I had employed in my graduate work. I was concerned by this from a measure theoretic sense since I could not conceive of how to deal with a complex measure. I asked professor Donsker if, in a sense, the Feynman path integral didn’t really exist—in a rigorous mathematical way, at any rate. He gave me a kind of puckish glance and quickly responded, yes!
I have to say this took the wind out of my sails at the time. Now, I was never anywhere Donsker’s league so I might not have fully understood his response. Perhaps he was responding to the naïve question of a student; in effect saying, “As you understand such things they don’t exist.� Presumably if I continued to pursue a study of such things I would learn the true nature of their existence. I’ll never know as my interest in the subject did largely subside.
In retrospect the power and excitement of Feynman and Hibbs lies not in its mathematical rigor but in its “visual appeal,� its tour de force of imagination. Most of Feynman’s contributions to physics have this quality. His imaginative power forces itself upon you so that you have the feeling that you too are discovering something wonderful. Feynman wants you with him, so to speak. To see what he sees is so compelling that questions of relative intellect (between mine and his) matter little as long as I share his sense of bedazzlement. That is why his famous Feynman Lectures remain popular and inspiring to this day.
It was this plus the fact that Feynman's novel approach to quantum mechanics seemed to tie in with almost every then-emerging sensational theory--fractals, chaos, path-integrals--that made this book a sort of bible to me during my graduate days. My copy has a lot of surface wear and the edges are dogged from years of being carried in my knapsack. And the pages are full of marginal notes written in as tiny script as I could manage using a narrow gauge mechanical pencil.
Since that time much of the text is probably mainstream--part of the standard curriculum of physics and mathematical physics. But it was still new then. Kind of like the Beatles today. They're still immensely popular but only those conscious of the spirit of the mid-1960's will have experienced the "inner quiver" of their arrival (something not always well received, by the way).
I don't know how this happened but it doesn't seem to be unrelated to the special nature of this book and the life of that titan of physics, Richard Feynman. As is well known, Feynman was a colorful character--what we used to call "a character"--and it wouldn't surprise me if he put Dr. Hibbs up to it.
I can no longer review this book in a technical sense; having moved on from physics almost 30 years ago. But I can give a flavor of what it was like to read it. To appreciate its thrill one must recall that in those days, the classical interpretation of quantum mechanics was very much in sway. It was strictly probabilistic and students were told there was no point in trying to imagine some underlying process governing the probabilities. Case closed. Sure there were individual physicists--some of great repute--who viewed quantum theory from novel angles. Alfred Lande was one, David Bohm another and even Dirac had proffered some interesting musing in his classic textbook on the subject. There was the quirky and famous EPR paper which put forth its (in)famous paradox; but most workers had little time for what seemed a speculative matter best left to those who had achieved the leisure and reputation to worry about it. It was a time when people, like Roger Penrose, with their lively interpretations of the wavefunction and their subsequent influence were still in the future.
Along comes (to me) Richard Feynman who, in 1948, wrote this totally wacky paper which, as I recall, began with the question of how one could integrate with respect to an infinite number of variables. For me, its immediate appeal came, not from its physics, but from the fact that Feynman had appeared to pose a genuine problem in the theory of the integral--something that I was very much infatuated with at the time. I too had wondered about this but lacked the technical skill and imagination to bring it beyond mere "bathtub cogitation." So I was very eager to know how this could be done. I had grasped the magnificent Lebesgue theory for finite dimensional spaces; how it gave meaning to the integration of functions "too pathological" for the Riemann approach. Was it possible that Feynman had delivered us an integral for infinite dimensional spaces too? Would it too shed light on even weirder functions--functions that had an infinite number of variables?...
In a sense the answer was that it did, though it had been provided decades before Feynman’s own work. Nor did he probably understand the technical difficulties involved from a measure theoretic perspective. In fact, it was Norbert Weiner who first broke ground in this area by formulating what is now called the Weiner measure. The Weiner process and its associated measure, partly intended as a mathematical representation of Brownian motion, gave rise to truly weird functions indeed. They were continuous everywhere while at the same time being differentiable nowhere. How much more pathologic can one get! It takes some thought to imagine such functions, unlike ordinary functions, because they consist of realizations which look somewhat like ordinary functions when graphed until one understands the fact that another graph of the same function will look completely different because it is a different realization. Another bizarre property is today called self-similarity in much the same sense as fractals. There are a host of other bizarre properties of such functions which, because of their technical nature, I won’t mention here.
I mentioned that Feynman probably did not fully understand the subtle nature of his mathematical invention. Unlike the Weiner measure, the measure associated with “Feynman’s process� can be considered a complex measure—sort of. I once took a class in stochastic integration from the renowned Monroe Donsker. After several class periods laying the ground work for the Weiner process and, in fact, deriving the Feynman-Kac formula (a beautiful formula!) which looks very much like a path-integral, I realized the relation between the two was that the latter can be transformed into the former via an imaginary time transformation—just as the Schrödinger equation becomes a diffusion equation, which I had employed in my graduate work. I was concerned by this from a measure theoretic sense since I could not conceive of how to deal with a complex measure. I asked professor Donsker if, in a sense, the Feynman path integral didn’t really exist—in a rigorous mathematical way, at any rate. He gave me a kind of puckish glance and quickly responded, yes!
I have to say this took the wind out of my sails at the time. Now, I was never anywhere Donsker’s league so I might not have fully understood his response. Perhaps he was responding to the naïve question of a student; in effect saying, “As you understand such things they don’t exist.� Presumably if I continued to pursue a study of such things I would learn the true nature of their existence. I’ll never know as my interest in the subject did largely subside.
In retrospect the power and excitement of Feynman and Hibbs lies not in its mathematical rigor but in its “visual appeal,� its tour de force of imagination. Most of Feynman’s contributions to physics have this quality. His imaginative power forces itself upon you so that you have the feeling that you too are discovering something wonderful. Feynman wants you with him, so to speak. To see what he sees is so compelling that questions of relative intellect (between mine and his) matter little as long as I share his sense of bedazzlement. That is why his famous Feynman Lectures remain popular and inspiring to this day.
It was this plus the fact that Feynman's novel approach to quantum mechanics seemed to tie in with almost every then-emerging sensational theory--fractals, chaos, path-integrals--that made this book a sort of bible to me during my graduate days. My copy has a lot of surface wear and the edges are dogged from years of being carried in my knapsack. And the pages are full of marginal notes written in as tiny script as I could manage using a narrow gauge mechanical pencil.
Since that time much of the text is probably mainstream--part of the standard curriculum of physics and mathematical physics. But it was still new then. Kind of like the Beatles today. They're still immensely popular but only those conscious of the spirit of the mid-1960's will have experienced the "inner quiver" of their arrival (something not always well received, by the way).
April 4, 2018
I enjoy challenging myself and keeping my brain working with books on Math, even if I don't always understand how everything works out. This is a great book to keep one calculating.
Read
December 19, 2022I don't know how you'd really star rate this. This book is an outline of Feynman's path integral formulation of quantum mechanics (with his PhD student Hibbs). A fascinating read, but also something of a frustrating one. Feynman and Hibbs aren't really interested in interpretations of the path integral, just its mathematical utility for solving certain classes of problem - which are limited and usually cumbersome. They do however provide a full treatment of the double slit experiment from the path integral perspective, which seems to produce the expected waviness and interference without needing to actually introduce waves into the problem. Could path integrals (or more strictly, the kernel derived from the integral) replace wavefunctions more generally? Possibly, although Feynman couldn't prove it.
April 12, 2016
Feynman the genius had found the way to rebuild quantum mechanics from classical mechanics. Bastard, he did that at the age younger than the age I study his stuff.
A lot of math is waiting for you ahead. You have been warned.
A lot of math is waiting for you ahead. You have been warned.
April 15, 2015
فاينمان هذا العبقري الاستثنائي عندما يمتعك فى ميكانيكا الكم
لم انهي الكتاب بل قرأته بطريقة تخطي ما لا يهمني معرفته ولم يكن بالقليل لكن بالمجمل ما قرأته كان ما احتاجه للاستزادة فى دراستي
هذا العبقري تستمتع له عندما تقرأ ما أبدعه فما بالك بشرحه هو الذي لا يقل ابداعاٌ وعبقرية عن انجازاته
لم انهي الكتاب بل قرأته بطريقة تخطي ما لا يهمني معرفته ولم يكن بالقليل لكن بالمجمل ما قرأته كان ما احتاجه للاستزادة فى دراستي
هذا العبقري تستمتع له عندما تقرأ ما أبدعه فما بالك بشرحه هو الذي لا يقل ابداعاٌ وعبقرية عن انجازاته
January 5, 2017
This book can give you the shortest route to Schrodinger's equation, and in a limited sense, to Dirac's equation. Feynman talks clearly and without introducing unnecessary math.
June 25, 2020
Basically a fun version of a textbook. I thoroughly enjoyed it but cant imagine anyone reading this particular book without already knowing QM and advanced calculus (to some degree).
June 14, 2020
Not give anything away, the non-differentiable paths are a typical indicator of quantum me-
mechanical effects. In classical mechanics the paths are linear and smooth instead. Brilliant! A most read in order to understand the big differences between classical and quantum effects.
mechanical effects. In classical mechanics the paths are linear and smooth instead. Brilliant! A most read in order to understand the big differences between classical and quantum effects.
October 19, 2017
This is my first book on quantum mechanics (which is unusual, often people start from more traditional books). I still enjoy every bit of this book.
May 11, 2018
This book is a masterpiece of clarity and is a brilliant blend of profound physics and mathematics. Thank you Richard P. Feynman (May 11, 1918 - Feb. 15, 1988)!
Want to read
July 1, 2009recommended follow up to path integral intro from Shankar
June 19, 2013
No point in reviewing a book I was required to read.
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