

Quantum mechanics for mathematicians - hhm
http://www.scottaaronson.com/democritus/lec9.html

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ced
I had to use Griffith's book, and he certainly didn't follow the historical
approach. He writes out Schrodinger's equation on the first page, before
moving on to "simple" examples (the infinite well). The hydrogen atom is
covered after a 100 pages or so.

[http://www.amazon.com/Introduction-Quantum-Mechanics-
David-G...](http://www.amazon.com/Introduction-Quantum-Mechanics-David-
Griffiths/dp/0131244051)

I love Griffith's informal style, and I'd recommend the book. Familiarity with
PDEs and harmonic oscillation would be the only necessary prerequisites I can
think of.

~~~
pfedor
Very few textbooks follow the historical approach as far as I can tell. The
author gives a false account of the way Quantum Mechanics is typically taught.

~~~
mechanical_fish
No, I think Schroedinger's equation is exactly what Prof. Aaronson is
complaining about. It's part of "the complicated patchwork of ideas invented
between 1920 and 1926". (The equation was published in 1926.) Teaching the
Schroedinger equation first _is_ the historical approach.

Consider this sentence from Wikipedia:

"The Schroedinger equation defines the behaviour of \psi\;, but does not
interpret what \psi\; is. Schroedinger tried unsuccessfully to interpret it as
a charge density. In 1926 Max Born, just a few days after Schroedinger's
fourth and final paper was published, successfully interpreted \psi\; as a
probability amplitude, although Schroedinger was never reconciled to this
statistical or probabilistic approach."

What this tells us is that Schroedinger's equation was a hack. It gave Erwin
the right answer, but he didn't know what it meant. And, lo and behold, when I
learned quantum mechanics in school I didn't know what the equation meant,
either -- I was so busy trying to solve the differential equation, and
learning about the relationship between the quantum Hamiltonian and the
classical Hamiltonian, and looking up complicated Bessel functions, and being
confused by angular momentum quantum numbers that I never really understood
what the hell the wave function actually represented.

Aaronson's point is that we now know that quantum mechanics is about
probability theory. Once you understand that -- complete with bras, kets,
state vectors and matrices -- you are better equipped to understand the
Schroedinger equation as one particular application of quantum theory.

I wish I'd known this guy back when I was a first-year physics grad student.

~~~
pfedor
I don't see how one can interpret the first paragraph as referring to the
Schroedinger equation:

"The first way -- which for most physicists today is still the only way --
follows the historical order in which the ideas were discovered. So, you start
with classical mechanics and electrodynamics, solving lots of grueling
differential equations at every step. Then you learn about the "blackbody
paradox" and various strange experimental results, and the great crisis these
things posed for physics. Next you learn a complicated patchwork of ideas that
physicists invented between 1900 and 1926 to try to make the crisis go away.
Then, if you're lucky, after years of study you finally get around to the
central conceptual point: that nature is described not by probabilities (which
are always nonnegative), but by numbers called amplitudes that can be
positive, negative, or even complex."

It's hardly possible to even write the Schroedinger's equation on the
blackboard without revealing the "central conceptual point" that complex
numbers are involved.

The "grueling differential equations" phrase refers to classical mechanics and
electrodynamics. This part is actually true, you typically learn some
classical mechanics and electrodynamics before you start QM.

~~~
mnemonicsloth
He describes my experience in undergrad physics (and graduate engineering)
pretty well. You get some examples to motivate a new theory, and then they
jump right to the Schrodinger equation and expect you to fall back on what you
know about turning the crank in boundary value problems. I didn't hear the
word 'Hermitian' for a long time.

------
jey
That was delicious. I've always avoided studying physics because it seems like
very hard work to just satisfy my curiosity... so far my copy of the _Feynman
Lectures_ has only served an ornamental purpose.

~~~
ashu
"Quantum Information and Quantum Computation" by Nielsen and Huang is also a
fascinating book if you want to look at Quantum Mechanics from a distinctly
mathematical and CS perspective.

~~~
michael_nielsen
I'm Michael Nielsen (the first author). I'm very glad you liked our book! A
little correction: my co-author is Ike Chuang.

(I'm not grepping my name. I've taken an extended, possibly permanent, break
from quantum computing, and will likely start a web-based company or
foundation. YC News is a great resource, which I check regularly.)

~~~
sarosh
Out of curiosity, will you be applying any principals from the book to the
startup?

~~~
michael_nielsen
The startup won't be quantum related, if that's what you're asking. Of course,
there is a lot that I learnt in the course of writing the book that will be
useful - techniques related to skills like abstraction, communication,
synthesis, and managing large projects.

