
Feynman’s Derivation of the Schrödinger Equation - luisb
http://fermatslibrary.com/s/feynmans-derivation-of-the-schrodinger-equation
======
spdustin
Not 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."

~~~
EGreg
"Rings a bell." Hah

~~~
malanj
Actually both parts are a joke, but only if you don't look for it.

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kurthr
I 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.p...](http://cds.cern.ch/record/101498/files/Thesis-1942-Feynman.pdf?version=1)

It's short at 74 book pages, and relatively readable.

~~~
ahuibers
The actual thesis is fun to look at! A typeset version is available:
[http://www.amazon.com/Feynmans-Thesis-Approach-Quantum-
Theor...](http://www.amazon.com/Feynmans-Thesis-Approach-Quantum-
Theory/dp/9812563806)

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theophrastus
Here's a link for the (download-able) pdf:
[http://www.physics.utah.edu/~starykh/phys7640/Lectures/Feynm...](http://www.physics.utah.edu/~starykh/phys7640/Lectures/FeynmansDerivation.pdf)

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giardini
Apparently 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=...](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)

~~~
acqq
Can you please write which woman and how she was involved? I failed to find
that in the linked material.

~~~
theoh
"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-q...](http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-quantum-
mechanics.html?pagewanted=all)

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cyphar
The 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
A 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
I 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).

------
wyager
Where 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.

~~~
77pt77
For 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

~~~
randlet
It's been a long time now, but I pretty much agree with you. I really enjoyed
Griffiths as an introduction but for reasons that escape me now I remember
having a bad time with Shankar.

~~~
77pt77
Griffiths is not great but for someone completely unfamiliar with the subject
it will hold your hand quite nicely and is not pretentious at all.

For someone a little more knowledgeable it might get a bit boring...

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spikels
This was written by a high school physics teacher. Very cool.

~~~
thinkpad20
He was actually my high school physics teacher! And very good. A really cool
guy and super smart.

~~~
evancharles
whoa.. I think we were literally in the same class at Lab. Nice to see you
here!

~~~
thinkpad20
oh, hey man! likewise! it's been a while. :)

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amai
That'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.

~~~
cbd1984
[http://signallake.com/innovation/DysonMaxwell041989.pdf](http://signallake.com/innovation/DysonMaxwell041989.pdf)

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evancharles
Btw, David Derbes, the writer, is perhaps the most overqualified high school
physics teacher there is. (He was my teacher.)

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sriku
This 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)

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mrcactu5
Feynman's "Quantum Mechanics and Path Integrals" is about $18 on Amazon

[http://www.amazon.com/Quantum-Mechanics-Path-Integrals-
Emend...](http://www.amazon.com/Quantum-Mechanics-Path-Integrals-
Emended/dp/0486477223)

That is a serious graduate level book - written in his own style.

~~~
beezle
I 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.

