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Greg Bernhardt said:This is why, in previous threads in PF, I disagree that we should teach students the concepts of QM FIRST, rather than the mathematical formulation straightaway.
atyy said:Hmmm, I still can't derive the Stefan-Boltzmann whatever - chills down my spine. How is that easy?
WannabeNewton said:What
atyy said:Is it easy?
WannabeNewton said:Indeed one of the professors I know basically called Griffiths' book a cookbook in differential equations.
WannabeNewton said:Im actually not sure what youre referring to. Are you talking about the Stefan Boltzmann law of radiation? I am not sure what that has to do with undergrad QM apart from historical impetus but there is a particularly lucid derivation in section 9.13 of Reif if youre interested. It's more of a statistical mechanics derivation. Which is good because statistical mechanics, both classical and quantum, is actually extremely interesting at the undergrad level.
Well, the historic approach is bad. You are taught "old quantum mechanics" a la Einstein and Bohr only to be adviced to forget all this right away when doing "new quantum mechanics". I've never heard that it is a good didactical approach to teach something you want the students to forget. They always forget inevitably most important things you try to teach them anyway, but in a kind of Murphy's Law they remember all the wrong things being taught in the introductory QM lecture.WannabeNewton said:Honestly I think at the undergraduate level QM is the easiest physics class one has to take. It is just a cookbook on calculations. Every book is uninspired and my class was certainly uninspired. It is an incredibly boring subject at this level. So I don't think difficulty is the issue. It is simply the lack of physical concepts and a healthy dose of philosophy that is avoided when teaching QM at the undergraduate level. Indeed one of the professors I know basically called Griffiths' book a cookbook in differential equations. A good book can go a long way. For me the saving grace was Landau and Lifshitz. It is the sole reason I started liking QM. Seriously the way undergrad QM is taught really isn't fun for the students. Boredom from a lack of intellectusl stimulation really isn't how a physics class should be.
vanhees71 said:Well, the historic approach is bad. You are taught "old quantum mechanics" a la Einstein and Bohr only to be adviced to forget all this right away when doing "new quantum mechanics". I've never heard that it is a good didactical approach to teach something you want the students to forget. They always forget inevitably most important things you try to teach them anyway, but in a kind of Murphy's Law they remember all the wrong things being taught in the introductory QM lecture.
May be QM is primarily predictive. Quantum mechanics construed as a predictive structure. After we try to interpret it with épistemic or ontological human sense.WannabeNewton said:It is just a cookbook on calculations.
microsansfil said:May be QM is primarily predictive. Quantum mechanics construed as a predictive structure. After we try to interpret it with épistemic or ontological human sense. For example "The debate on the interpretation of quantum mechanics has been dominated by a lasting controversy between realists and empiricists" : http://michel.bitbol.pagesperso-orange.fr/transcendental.html
bhobba said:And I really do mean IDEA - not ideas - see post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.
probably not theory, but the people :bhobba said:I think philosophers worry more about that sort of thing more than physicists or mathematicians.
microsansfil said:Erwin Schrodinger : Mind and matter - What Is Life? - My View of the World - ...Werner Heisenberg : Physics and Philosophy: The Revolution in Modern Science - Mind and Matter - The physicist's conception of nature - ...
To understand the quantum theory in terms of mathematical language, we have in "France" some good free lecture like this one from "Ecole polytechnique" : http://www.phys.ens.fr/~dalibard/Notes_de_cours/X_MQ_2003.pdfbhobba said:But of relevance to this thread you will get a lot more out of that book if you know some of the real deal detail.
vanhees71 said:If you want to rise interpretational problems at all, you shouldn't do this in QM 1 or at least not too early. First you should understand the pure physics, and that's done with the minimal statistical interpretation. If you like Landau/Lifshits (all volumes are among the most excellent textbooks ever written, but they are for sure not for undergrads; this holds also true for the also very excellent Feynman lectures which are clearly not a freshmen course but benefit advanced students a lot), I don't understand why you like to introduce philosophy into a QM lecture. This book is totally void of it, and that's partially what it makes so good ;-)).
stevendaryl said:When discussing the best approach to teaching something like quantum mechanics, I think you really have to consider the purpose in teaching it...
Barry911 said:no observables, no predictions...sounds like an elegant theory of pure mathematics.
Barry911 said:Problem:
The outcome of single quantun outcomes does not yield a meaningful outcome. Iteration of "identical
experiments" yields probability densities. P-densities do not predict where a quantum event will occur
only statistical weightings
Greg Bernhardt said:We use the identical words such as particle, wave, spin, energy, position, momentum, etc... but in QM, they attain a very different nature. You can't explain these using existing classical concepts.
thegreenlaser said:When someone finally explained that you can't really understand quantum mechanics in terms of classical mechanics, I felt like I was finally able to start learning.
Barry911 said:The outcome of single quantun outcomes does not yield a meaningful outcome. Iteration of "identicalexperiments" yields probability densities. P-densities do not predict where a quantum event will occur only statistical weightings
thegreenlaser said:My 3rd year quantum prof explained this concept in his first lecture, and that was a very big "aha" moment for me. Up until then, all my teachers had tried to explain quantum mechanics in terms of classical mechanics, and it never quite made sense. When someone finally explained that you can't really understand quantum mechanics in terms of classical mechanics, I felt like I was finally able to start learning.
Barry911 said:Do you find a fundamental problem with the idea that the wave function represents a pure probability description (Born) and yet represents all the information defining the "particle" of interest?
Barry911 said:I have a problem with the word "determinism" it seems to imply the cause-effect relation of Newton
Barry911 said:Also thanks for the recurring reference to Bellentine! I just bought the book. I've just finished the math chapterand thought it excellent. It seems like a "superposition" of a textbook and an advanced popularizer.
Among the traditional interpretations, the statistical interpretation discussed by
L.E. Ballentine,
The Statistical Interpretation of Quantum Mechanics,
Rev. Mod. Phys. 42, 358-381 (1970)
is the least demanding (it assumes less than the Copenhagen interpretation and the Many Worlds interpretation) and the most consistent one.
The statistical interpretation explains almost everything, and only has the disatvantage that it explicitly excludes the applicability of QM to single systems or very small ensembles (such as the few solar neutrinos or top quarks actually detected so far), and does not bridge the gulf between the classical domain (for the description of detectors) and the quantum domain (for the description of the microscopic system).
In particular, the statistical interpretation does not apply to systems that are so large that they are unique. Today no one disputes that the sun is governed by quantum mechanics. But one cannot apply statistical reasoning to the sun as a whole. Thus the statistical interpretation cannot be the last word on the matter.
http://arnold-neumaier.at/physfaq/topics/mostConsistent
I chose not to label the "ensemble interpretation" as correct because the ensemble interpretation makes the claim that only the statistics of the huge repetition of the very same experiment may be predicted by quantum mechanics. This is a very "restricted" or "modest" claim about the powers of quantum mechanics and this modesty is actually wrong. Even if I make 1 million completely different experiments, quantum physics may predict things with a great accuracy.
Imagine that you have 1 million different unstable nuclei (OK, I know that there are not this many isotopes: think about molecules if it's a problem for you) with the lifetime of 10 seconds (for each of them). You observe them for 1 second. Quantum mechanics predicts that 905,000 plus minus 1,000 or so nuclei will remain undecayed (it's not exactly 900,000 because the decrease is exponential, not linear). The relatively small error margin is possible despite the fact that no pair of the nuclei consisted of the same species!
So it's just wrong to say that you need to repeat exactly the same experiment many times. If you want to construct a "nearly certain" proposition – e.g. the proposition that the number of undecayed nuclei in the experiment above is between 900,000 and 910,000 – you may combine the probabilistically known propositions in many creative ways. That's why one shouldn't reduce the probabilistic knowledge just to some particular non-probabilistic one. You could think it's a "safe thing to do". However, you implicitly make statements that quantum mechanics can't achieve certain things – even though it can.
http://motls.blogspot.ie/2013/01/poll-about-foundations-of-qm-experts.html
bolbteppa said:Regarding Ballentine, are these claims really true:
bolbteppa said:They seem like pretty fatal flaws to me, or at least good reasons to choose Landau instead of this potentially shaky stuff...
atyy said:Ballentine is the most misleading book on quantum mechanics I have ever read.