4 ms·

Quantum mechanics for mathematicians

34 points by hhm 19y ago

jey 19y ago
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 19y ago
  "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.
  - jey 19y ago
    Awesome, thanks!
  - michael_nielsen 19y ago
    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.)
    - deleted 19y ago
      [deleted]
    - sarosh 19y ago
      Out of curiosity, will you be applying any principals from the book to the startup?
      - michael_nielsen 19y ago
        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.
ced 19y ago
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-Griffiths/dp/0131244051 http://www.amazon.com/Introduction-Quantum-Mechanics-David-G... 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 19y ago
  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 19y ago
    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.

34 points by hhm 19y ago

jey 19y ago

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 19y ago
"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.
- jey 19y ago
  Awesome, thanks!
- michael_nielsen 19y ago
  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.)
  - deleted 19y ago
    [deleted]
  - sarosh 19y ago
    Out of curiosity, will you be applying any principals from the book to the startup?
    - michael_nielsen 19y ago
      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.

ced 19y ago

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-Griffiths/dp/0131244051 http://www.amazon.com/Introduction-Quantum-Mechanics-David-G... 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 19y ago
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 19y ago
  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.