7 ms·
Feynman’s Derivation of the Schrödinger Equation
- theophrastus 11y agoHere's a link for the (download-able) pdf: http://www.physics.utah.edu/~starykh/phys7640/Lectures/FeynmansDerivation.pdf http://www.physics.utah.edu/~starykh/phys7640/Lectures/Feynm...
- giardini 11y agoApparently Schrodinger _guessed_ his equation. Not that it was an easy guess - a woman was involved. See p. 547 of "Quantum Foundations and Open Quantum Systems:Lecture Notes of the Advanced School" https://books.google.com/books?id=LVICCwAAQBAJ&pg=PA547&lpg=PA547&dq=schrodinger+guessed+his+equation&source=bl&ots=7JTetjnUdo&sig=y2cYDRiTm4S6Jo7faIQoq-sJC4c&hl=en&sa=X&ved=0ahUKEwi0stmbn8jKAhUD6aYKHY21D_8Q6AEIIjAE#v=onepage&q=schrodinger%20essentially%20guessed&f=false https://books.google.com/books?id=LVICCwAAQBAJ&pg=PA547&lpg=...
- acqq 11y agoCan you please write which woman and how she was involved? I failed to find that in the linked material.
- theoh 11y ago"A few days before Christmas, 1925, Schrodinger, a Viennese-born professor of physics at the University of Zurich, took off for a two-and-a-half-week vacation at a villa in the Swiss Alpine town of Arosa. Leaving his wife in Zurich, he took along de Broglie's thesis, an old Viennese girlfriend (whose identity remains a mystery) and two pearls. Placing a pearl in each ear to screen out any distracting noise, and the woman in bed for inspiration, Schrodinger set to work on wave mechanics. When he and the mystery lady emerged from the rigors of their holiday on Jan. 9, 1926, the great discovery was firmly in hand." http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-quantum-mechanics.html?pagewanted=all http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-q...
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- spikels 11y agoThis was written by a high school physics teacher. Very cool.
- thinkpad20 11y agoHe was actually my high school physics teacher! And very good. A really cool guy and super smart.
- evancharles 11y agowhoa.. I think we were literally in the same class at Lab. Nice to see you here!
- thinkpad20 11y agooh, hey man! likewise! it's been a while. :)
- wyager 11y agoWhere did we get that [Schrödinger's equation] from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger. -The Feynman Lectures on Physics For anyone who wants to study quantum mechanics and has a math background, I strongly recommend Shankar's quantum textbook. It has the most rigorous, clear, and correct derivations I have seen thus far, starting with vector spaces and moving to physical systems only after a hundred or so pages.
- danharaj 11y agoHave you ever read Lectures on Quantum Mechanics for Mathematics Students or Quantum Mechanics for Mathematicians? I'd like to know how Shankar's book sits in the space of QM textbooks.
- 77pt77 11y agoShankar is all round a very practical book to pass quals, very poorly structured, highly pretentious by dealing with say parth integrals with grassman variables but doing an awful job at basic stuff such as adding angular momentum. If you've got a math background I'd recommended you skip Shankar even more vehemently than I usually do.
- 77pt77 11y agoFor the love of God, do not use Shankar! The book is just down right atrocious. The fact that it became almost standard in American universities speaks more of the power of networking than anything else. Shankar's book is anything but rigorous, quite on the contrary. There are so many good QM books: For an absolute beginner I'd recommend David Griffiths Dirac's is very readable Sakurai's is very good though a bit advanced Whatever you do, it's difficult to go wrong by not using Shankar's
- foob 11y agoI personally think that Shankar makes a great companion to Sakurai. Shankar is less rigorous but it explains things in a more accessible way which can be extremely helpful if you find Sakurai too terse on some topics.
- kurthr 11y agoI find that often reading a scientist's dissertation will often tell you something about how they approach the rest of their research. Somewhere I actually have a paper copy of Feynman's Thesis under Wheeler, which covers exactly this material. He was clearly enamored of Lagrangian formulations quite early (I didn't know that it was due to a High School teacher). You can find this actual thesis on-line at CERN: http://cds.cern.ch/record/101498/files/Thesis-1942-Feynman.pdf?version=1 http://cds.cern.ch/record/101498/files/Thesis-1942-Feynman.p... It's short at 74 book pages, and relatively readable.
- santaclaus 11y ago> I didn't know that it was due to a High School teacher That's one badass high school physics teacher! Ours grew pale at the mention of a derivative, let alone calculus of variations.
- ahuibers 11y agoThe actual thesis is fun to look at! A typeset version is available: http://www.amazon.com/Feynmans-Thesis-Approach-Quantum-Theory/dp/9812563806 http://www.amazon.com/Feynmans-Thesis-Approach-Quantum-Theor...
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- mrcactu5 11y agoFeynman's "Quantum Mechanics and Path Integrals" is about $18 on Amazon http://www.amazon.com/Quantum-Mechanics-Path-Integrals-Emended/dp/0486477223 http://www.amazon.com/Quantum-Mechanics-Path-Integrals-Emend... That is a serious graduate level book - written in his own style.
- ahuibers 11y agoThis article might be one of the best intros: Space-Time Approach to Non-Relativistic Quantum Mechanics R. P. Feynman Rev. Mod. Phys. 20, 367 – Published 1 April 1948 Caltech has this available: http://authors.library.caltech.edu/47756/1/FEYrmp48.pdf http://authors.library.caltech.edu/47756/1/FEYrmp48.pdf There are some other good treatments too, although I can't find them at the moment.
- beezle 11y agoI think I would rather my copy of the original hard cover w/ published corrections. "...recasts many equations for clearer comprehension" to me is an unacceptable modification.
- cyphar 11y agoThe Schrödinger equation was not derived, a more accurate word would be guessed. It's a fundamental law, like F = ma (although that is actually more of a definition than a law). There is no fundamental explanation why electrons obey the Schrödinger equation, just like there's no fundamental explanation why macroscopic objects obey F = ma.
- krastanov 11y agoA lot of things can be derived from more basic or at least more beautiful principles. It makes perfect sense to say that Schroedinger's equation can be derived from Lagrangian Mechanics, even if this is not historically how it happened. An especially beautiful constraint is "Schroedinger's equation has to be linear because otherwise you can build a (quantum) computer that can solve NP-complete problems in polynomial time". Schroedinger did not know about NP-completeness, but this notion does give us clues why the equation is what it is. It is always instructive to see how a "fundamental" law can be derived or at least constrained from other laws. Thermodynamics and the notion of entropy would not have been invented if engineers did not "rederive" what was considered fundamental at the time.
- nilkn 11y agoI think you're both right. The grandparent post is right in the sense that reductionism always reduces, ultimately, to a guess (in this case, Lagrangian mechanics is the guess). You're right, though, in that a basic framework can be established, using minimal assumptions and axioms, in which most of classical physics and even much of quantum physics can be derived via (mostly) rigorous mathematical arguments. But that framework itself is, at the end of the day, a guess. It's simply the best guess we have at the given moment in time that fits the evidence (e.g., by allowing us to derive from it known rules and patterns that past generations have verified fit the evidence).
- calhoun137 11y agoIt's actually not true to say that Schrodinger's equation, or F=ma, cannot be derived. This is because in order to derive something, you need to first start from a set of assumptions. You can pick any assumptions you want, that is your privilege, as it is mine. If you want F=ma to be an assumption, you can go on and derive things from that. But truly, F=ma is not the most general assumption in theoretical physics. If you look in any decent book on classical mechanics, you will find that F=ma in fact is derived from a much more general principle, the Lagrangian. That is the same Lagrangian that is the subject of the OP, which is used to derive the Schrodinger equation; and it's not just a coincidence.
- spdustin 11y agoNot many people know that Schrödinger wrote a a paper involving a dog, and to show solidarity with a fellow scientist, opted to model the dog after a subject of Pavlov's experiments. I called the UIUC library to ask if they had a copy of the paper just a few months ago, but I couldn't remember the title of the paper. The researcher that answered told me, "That sure rings a bell; I'm not sure if it's here or not, though."
- evancharles 11y agoBtw, David Derbes, the writer, is perhaps the most overqualified high school physics teacher there is. (He was my teacher.)
- sriku 11y agoThis is goosebump material! It is fascinating how concepts from classical mechanics port over into quantum mechanics. If we'd stuck with F=ma, perhaps we may not have gone far. However, the Hamiltonian and Lagrangian approaches are sweet ports. Noether's theorem [1] connects symmetries of a lagrangian with corresponding conservation laws. Time translation symmetry implies energy conservation. Space translation symmetry implies momentum conservation in the direction of translation. This ports directly to QM. Feynman, in his lecture series, mentions another such symmetry - phase translation symmetry - that exists for QM actions and asks what conservation law does that correspond to. It is the conservation of charge. Mind blown! [1]: https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org/wiki/Noether%27s_theorem
- amai 11y agoThat's nothing: Feynman's proof of the Maxwell equations (FJ Dyson - Phys. Rev. A, 1989 (http://signallake.com/innovation/DysonMaxwell041989.pdf) http://signallake.com/innovation/DysonMaxwell041989.pdf)) shows, that it is possible to derive Maxwells equations from Newtons second law of motion and the uncertainty principle.
- Lawtonfogle 11y agoExtra ) in your link.
- cbd1984 11y agohttp://signallake.com/innovation/DysonMaxwell041989.pdf http://signallake.com/innovation/DysonMaxwell041989.pdf