# quantum mechanics history question **URL:** \ **Category:** Factual Questions\ **Created:** [April 16, 2009, 4:10pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298 "2009-04-16T16:10:43Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 16, 2009, 4:10pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/1 "2009-04-16T16:10:43Z")
There are two equivalent formulations of quantum mechanics: matrix mechanics, created by Werner Heisenberg in 1925, and wave mechanics, created by Erwin Schrödinger in 1926. But who proved they were equivalent, and in what year? > [@wikipedia article on Schrödinger](#): > > In January 1926, Schrödinger published in the Annalen der Physik the paper “Quantisierung als Eigenwertproblem” [tr. Quantization as an Eigenvalue Problem] on wave mechanics and what is now known as the Schrödinger equation. In this paper he gave a “derivation” of the wave equation for time independent systems, and showed that it gave the correct energy eigenvalues for the hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics, and indeed of all physics and chemistry. A second paper was submitted just four weeks later that solved the quantum harmonic oscillator, the rigid rotor and the diatomic molecule, and gives a new derivation of the Schrödinger equation. **A third paper in May showed the equivalence of his approach to that of Heisenberg** and gave the treatment of the Stark effect. > [@wikipedia article on John von Neumann](#): > > [von Neumann] immediately realized, in 1926, that a quantum system could be considered as a point in a so-called Hilbert space, analogous to the 6N dimension (N is the number of particles, 3 general coordinate and 3 canonical momentum for each) phase space of classical mechanics but with infinitely many dimensions (corresponding to the infinitely many possible states of the system) instead: the traditional physical quantities (e.g. position and momentum) could therefore be represented as particular linear operators operating in these spaces. The physics of quantum mechanics was thereby reduced to the mathematics of the linear Hermitian operators on Hilbert spaces. For example, the famous uncertainty principle of Heisenberg, according to which the determination of the position of a particle prevents the determination of its momentum and vice versa, is translated into the non-commutativity of the two corresponding operators. **This new mathematical formulation included as special cases the formulations of both Heisenberg and Schrödinger** , and culminated in the 1932 classic The Mathematical Foundations of Quantum Mechanics. > [@wikipedia article on Paul Dirac](#): > > Dirac’s Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. **In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödinger on wave mechanics into a single mathematical formalism** that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system. The book also introduced the delta function. Following his 1939 article, he also included the bra-ket notation in the third edition of his book, thereby contributing to its universal use nowadays. Also, can any of you recommend a good book on the history of quantum mechanics – particularly for someone like me who already is quite familiar with the physics? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [April 16, 2009, 4:29pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/2 "2009-04-16T16:29:31Z")
[The Age of Entanglement: When Quantum Physics Was Reborn, by Louisa Gilder](http://www.amazon.com/Age-Entanglement-Quantum-Physics-Reborn/dp/1400044170/ref=sr_1_1?ie=UTF8&s=books&qid=1239899281&sr=8-1) goes over the creation of QM understanding almost paper by paper. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 16, 2009, 7:21pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/3 "2009-04-16T19:21:50Z")
Thanks **Exapno**. Regarding my question about the equivalence of wave mechanics and matrix mechanics, the wikipedia article on Carl Eckart (which unlike some of the others cites the original papers) says Schrodinger and Eckart independently proved their equivalence. > [@wikipedia article on Eckart](#): > > When Erwin Schrödinger’s first paper[7] in the series of four[8] [9] [10] on the wave mechanics formulation of quantum mechanics was published in January, Eckart soon realized that the matrix formulation and wave formulation of quantum mechanics were equivalent; he submitted his paper[11] to the Proceedings of the National Academy of Sciences of the United States of America for publication. However, it was communicated on May 31, 1926, and Schrödinger’s paper[12] on the equivalence was received on March 18, 1926, thus giving him credit for the realization.[2] So I guess Schrödinger and Eckart are the real answers to my question, and the articles on Dirac and von Neumann are referring to their developing new approaches to quantum mechanics that encompass both the matrix and wave descriptions – e.g., Dirac’s bra-ket formalism, von Neumann’s axiomatic approach (observables are Hermitian operators, states are rays in a Hilbert space, etc.) ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 16, 2009, 7:42pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/4 "2009-04-16T19:42:40Z")
Anyway, even though I kind of answered my own question, I’d still be interested in any further suggestions of good books on the history of QM. ---
**Author:** ![Saltire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saltire/32/553_2.png) [@Saltire](https://boards.straightdope.com/u/Saltire)\ **Post date:** [April 16, 2009, 8:14pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/5 "2009-04-16T20:14:28Z")
I really love to read and re-read “The Second Creation” by Crease and Mann. It covers a lot of stuff, from the luminiferous ether to the elecroweak unification. So there’s plenty of particle stuff in with the quantum stuff. But it tells a lot of great stories along the way about the scientists themselves and the ways the science happened. A lot of personality conflicts and real-world interruptions that make it such a zigzag path. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [April 16, 2009, 9:21pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/6 "2009-04-16T21:21:35Z")
Everyone seems to think “Inward Bound” by Pais is great although I didn’t especially care for it. One I did like was “Conceptual Developments of 20th Century Field Theory” by Cao. It also should win an award for long titles. ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [April 16, 2009, 9:32pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/7 "2009-04-16T21:32:49Z")
Although I can’t attest for the rigor of the paper\*, [this article](http://philsci-archive.pitt.edu/archive/00003658/01/perovic_preprint.pdf) states that Schrödinger’s equivalence proof was quite inadequate (from a mathematical perspective, at least). A valid proof of the equivalence of matrix and wave mechanics was eventually developed by the smartest man who ever lived, John von Neumann, about five years later. - but, damn, it sure looks impressive! ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 10:06pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/8 "2009-04-16T22:06:15Z")
Fucking von Neumann. Set theory, mathematical logic, operator theory and quantum mechanics, game theory and economics, the Manhattan Project, computer architecture, cellular automata, mergesort… And here I am in my underwear not yet having eaten breakfast. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [April 16, 2009, 10:20pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/9 "2009-04-16T22:20:33Z")
> [@](#): > > The book also introduced the delta function. It’s interesting that when Dirac proposed this function (functional) mathematicians were outraged. Later when it turned out to be part of distribution theory (I think) they were duly impressed. (I think) ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 16, 2009, 11:10pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/10 "2009-04-16T23:10:05Z")
> [@KarlGauss](#): > > the smartest man who ever lived, John von Neumann It’s worth mentioning that your namesake was no dummy, either. I remember taking a survey of algebra course in college, taught by a German professor. At the time I had no idea about how Germans write a double-S. I spent most of the semester wondering how it was that I’d never heard of this “Gaub” guy, despite the fact that he basically invented modern number theory. Anyway, thanks for the link. I’ll defintely have a look at that article. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 16, 2009, 11:12pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/11 "2009-04-16T23:12:06Z")
> [@Indistinguishable](#): > > Fucking von Neumann. Set theory, mathematical logic, operator theory and quantum mechanics, game theory and economics, the Manhattan Project, computer architecture, cellular automata, mergesort… > > And here I am in my underwear not yet having eaten breakfast. You think that’s frustrating? I can only imagine how [Évariste Galois](http://en.wikipedia.org/wiki/Galois) must make you feel. The guy got himself killed in a duel at the age of 20 and _still_ somehow found time to invent his own branch of mathematics. ---
**Author:** ![bonzer](https://avatars.discourse-cdn.com/v4/letter/b/45deac/32.png) [@bonzer](https://boards.straightdope.com/u/bonzer)\ **Post date:** [April 16, 2009, 11:13pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/12 "2009-04-16T23:13:03Z")
> [@tim314](#): > > Also, can any of you recommend a good book on the history of quantum mechanics – particularly for someone like me who already is quite familiar with the physics? I’m going to stick my neck out and suggest that there really isn’t one. There are plenty of pop science books that will skim through the history without engaging in the technical details at the level your question was pitched at. There are plenty of biographical works that follow individual careers through the events; these range from the fairly non-technical, but excellent (say, Cassidy’s Heisenberg book) to the thorough, but mediocre (Enz’s Pauli bio). There are the various memoirs. There are detailed reconstructions of bits of the story (such as Kuhn’s _Black Body Theory …_). There are fairly detailed overviews of the story as part of a much wider narrative of twentieth century physics (e.g. _Inward Bound_). Handy compilations of important papers, usually with good commentaries. But beyond those substitutes you’re pretty much stuck. There is Mehra’s huge multi-volume affair, which does plod through everything, but is horrible and basically just amateurishly regurgitates its sources. It seems an obvious gap in the literature, though a non-trivial one to fill. A good single volume _The Origins of Quantum Mechanics, 1900-30_ that doesn’t shy away from the technicalities and tries to synthesise the whole story. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 11:34pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/13 "2009-04-16T23:34:46Z")
> [@tim314](#): > > You think that’s frustrating? I can only imagine how [Évariste Galois](http://en.wikipedia.org/wiki/Galois) must make you feel. The guy got himself killed in a duel at the age of 20 and _still_ somehow found time to invent his own branch of mathematics. Eh, he had one good idea. I can still aspire to that. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 16, 2009, 11:37pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/14 "2009-04-16T23:37:04Z")
That’s a shame, **bonzer**. It seems like more than once I’ve read a textbook that started with “The history of quantum mechanics is a fascinating one, and one that every student ought to familiarize themselves with. Unfortunately, that is beyond the scope of this book. Anyway, here’s the Schrödinger equation. :p” Although in fairness, the author usually doesn’t actually _type_ “:p”. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 17, 2009, 1:41am UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/15 "2009-04-17T01:41:33Z")
Since we’re talking about the founders of quantum mechanics, here are a few tidbits about them I find interesting (some taken from wikipedia, so take with an appropriately large grain of salt): Schrödinger and his wife had an “open” marriage (at some point she was actually involved with the eminent mathematician/physicist Hermann Weyl), for a while Schrödinger lived with both her and a second “wife” who was technically married to someone else. When Heisenberg first discovered matrix mechanics, he didn’t know that the equations he’d written down described matrices. Amazing as it is to anyone studying physics today, at the time matrices weren’t widely studied by physicists, being largely the domain of pure mathematicians. It was Heisenberg’s boss, Max Born, who discovered the connection to matrices, and he and his student Pascual Jordan fleshed out the details. Jordan, incidentally, was one of the most significant contributors to the early development of quantum mechanics _not_ to win the Nobel Prize. (Apparently both Einstein and Wigner nominated him at various times.) It’s been speculated that he was passed over for the prize in part because he had been a member of the Nazi Party. After the war Jordan sought a recommendation from Born, and Born (who was of Jewish heritage and had lost family in the holocaust) basically told him to take a hike. Born eventually won the Nobel for work he did without Jordan. Paul Dirac was a man of few words, who chose his words carefully. One of my favorite Dirac quotations concerns the difference between science and poetry: “In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite.” ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [April 17, 2009, 2:50am UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/16 "2009-04-17T02:50:06Z")
Pretty much all of what tim314 talks about is examined at length in Gilders’ book. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 17, 2009, 3:40am UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/17 "2009-04-17T03:40:54Z")
> [@KarlGauss](#): > > Although I can’t attest for the rigor of the paper\*, [this article](http://philsci-archive.pitt.edu/archive/00003658/01/perovic_preprint.pdf) states that Schrödinger’s equivalence proof was quite inadequate (from a mathematical perspective, at least). A valid proof of the equivalence of matrix and wave mechanics was eventually developed by the smartest man who ever lived, John von Neumann, about five years later. > > - but, damn, it sure looks impressive! OK, I just read the paper you cite. Here’s what I make of it: The author is responding to several other papers (recent papers by philosophers of science, not 1920’s era papers by physicists). As this author characterizes them, those papers are (1) arguing that Schrödinger’s proof and others prior to von Neumann weren’t rigorous, and (2) that this betrays some irrationality on the part of physicists for assuming the two theories had been proven equivalent. The author agrees with (1) but not with (2). The author basically replies: _Sure_, Schrödinger’s paper doesn’t rigorously prove the equivalence of the two, and in fact this would have been impossible until the formalism was developed further and more experiments clarified the appropriate assumptions for the theory to make. Rather, he says Schrödinger mostly set out to prove that wave mechanics could duplicate the successes of matrix mechanics, particularly with regard to spectral lines where the matrix theory seemed to have an advantage. Of course, in hindsight this agreement between wave mechanics and matrix mechanics is understood to be a consequence of the equivalence of the two theories. The author claims that it is with this hindsight that the paper is seen as a “proof” of the equivalence of these theories. The author argues that in fact the paper does prove what Schrödinger wanted, which was just to prove that the two theories give the same results in some specific cases of interest. ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [April 17, 2009, 4:44am UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/18 "2009-04-17T04:44:25Z")
**Tim** , I truly wish I had something intelligent to say in response to your precis and criticism. Alas, it is not be. As an aside, **Tim** , you are living proof that someone can be extraordinarily smart yet still be a nice guy (with the measure being in the form of two linked questions: Would I like to go out for a beer with the person? Would there be a good chance that he/she would comment sagaciously on the physical nature and the physics of the head/liquid interface?) Please don’t ever change! ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [April 17, 2009, 5:39am UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/19 "2009-04-17T05:39:43Z")
Wow, thanks **Karl**! I think that’s the nicest thing anyone on this board has ever said about me. (Which is not to suggest that the rest of you have been a bunch of meanies or anything . . . ) ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [April 17, 2009, 12:47pm UTC](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298/20 "2009-04-17T12:47:13Z")
Although the delta function is credited to Dirac, I have always believed that Oliver Heaviside was using something very like it in the 19th century. As a mathematician, I certainly feel a lot of sympathy for mathematicians who refused to believe anything “proved” using it until someone (Laurent Schwartz, to be precise) put it into a rigorous mathematical framework. As for Galois, it is highly unfair to say that he had one good idea. First, it was so original that it basically took 50 years before mathematics had developed enough to be able to understand it. Groups had to be invented first. Since then it has blossomed into an amazingly beautiful theory, with ramifications in many areas of mathematics. Incidentally, any mathematician with one good idea can be said to have had a successful career. As I look back on the 80 or so papers I have published, I realize that all but one of them consisted in extending someone else’s good idea just a bit further. The remaining paper had one new idea. It is staggering to imagine that Galois had one good idea at age 20 and we can only conjecture how many others he might have had had he lived. [Next page](https://boards.straightdope.com/t/quantum-mechanics-history-question/493298.md?page=2)