EPTQuantum Mechanics - Page 2
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rei
United States3594 Posts
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iamho
United States3347 Posts
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0x64
Finland4615 Posts
On April 01 2013 00:18 iamho wrote: I used to think quantum physics was awesome until I took a class on it.. Then I realized it was pretty much the standard "here's some equations someone smarter than you derived, manipulate them and do math" type of thing. Also I still have no idea what the conceptual explanation for matrices and eigenvectors are, despite acing the class. To the math purists out there, I'd say that as a non-physics major, the non-math explanations and the pop science I read were both far more engaging and useful than the equations. That's how I feel, I know how university physics is taught and I've seen it been taught almost precisely the same way all around the globe almost from the same books. There is something different when a Nobelist put his mind to work on how he could explain the things he understand to the people that don't need actually to understand the specific. Need I remind you guys, that this is the definition of a good scientific paper; one should be able to read a paper with a general understanding of the field or even better with a scientific general education. Well anyway, I tend, with time, to think there is more value on the way the message is delivered than university put effort into. And if a lecturer can't deliver the message better than a great lecturer, then record once the damn lecture and distribute it to the whole world. Have the lecturer use his hours on explaining and answering questions about the lecture instead of trying to produce something similar. | ||
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0x64
Finland4615 Posts
Electromagnetism, the math behind, all seems so disconnected. It is possible to learn how to calculate and yet not even understanding what you are doing and why. Scary? | ||
micronesia
United States24775 Posts
On April 01 2013 04:29 0x64 wrote: And physics, I believe is one of the most dependent area, where the quality of the lecturer can help you "get it". Electromagnetism, the math behind, all seems so disconnected. It is possible to learn how to calculate and yet not even understanding what you are doing and why. Scary? It is scarier when this happens in practical settings. For example, an engineer who is strong with computers may use matlab simulations to find solutions to problems without actually understanding the underlying issue causing the problem, and how this solution addresses (or shorts) them. | ||
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0x64
Finland4615 Posts
On April 01 2013 05:15 micronesia wrote: It is scarier when this happens in practical settings. For example, an engineer who is strong with computers may use matlab simulations to find solutions to problems without actually understanding the underlying issue causing the problem, and how this solution addresses (or shorts) them. Hah, now I'm scarred, thanks! | ||
Teoita
Italy12246 Posts
On the other hand, "uh, it seems like two operators don't commute here" is a great expression for when anything doesn't work as it should >.> | ||
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rei
United States3594 Posts
Nobody here can answer this? could it be that it is not every one of those 4% reflects into the detector, instead all of the photons who hits an atom gets absorbed if it's the right wave length, and only 4% of them gets absorbed and reflect and that percentage depends on the material since different material compose of different atoms and hence difference electron orbitals that requires different activation energy to make the electron go to excited state and then back to ground state and re-emit a photon in a random direction. and that 4% of photons gets re-emitted by the reflecting material's atoms will be traveling in random direction, yet because photon have wave property the only place these random directed photons didn't cancel each other's wave out is at the exact angle in which the sum of all vectors of those photons have the shortest path. If you put the detector at that exact place you would count 4% of the total photons and if you place that detector elsewhere you would count less than 4%? did i get this right? | ||
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felisconcolori
United States6168 Posts
Which is why I think the math is generally necessary. Some things mathematically let you see the logic behind and with the more imprecise English descriptions. And the English descriptions can get engaging and go right on into "WTF" land - but are still pretty damned cool. All else aside, I think QM is a pretty cool area of physics. Much cooler than all that string stuff. Actually, that sounds like a lot of engineering I know. They don't really care WHY something works the way it does - they are more concerned with what they can do with the properties available to them. If it works in whatever way it works, that's great, they can use that. If it doesn't impact what they are trying to do with something, they really aren't that interested in the deeper questions. A civil engineer only cares about how strong concrete is under specific conditions and if it is suitable for the application they're using it for - not why cement bonds together in the first place. | ||
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micronesia
United States24775 Posts
On April 01 2013 14:37 felisconcolori wrote: Actually, that sounds like a lot of engineering I know. They don't really care WHY something works the way it does - they are more concerned with what they can do with the properties available to them. If it works in whatever way it works, that's great, they can use that. If it doesn't impact what they are trying to do with something, they really aren't that interested in the deeper questions. A civil engineer only cares about how strong concrete is under specific conditions and if it is suitable for the application they're using it for - not why cement bonds together in the first place. Sometimes a lack of actual understanding of what's going on can have serious unforeseen consequences. Maybe this adjustment matlab told you to do makes the bridge stronger, but because you relied solely on the computer simulation and didn't actually analyze it yourself, you didn't realize that the bridge is now much more susceptible to resonance, weathering, or some thing your simulation didn't take into account. While common, this is quite a dangerous way to do science. | ||
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Teoita
Italy12246 Posts
Dr Cooper...Dr Koothrappali...Dr Hofstadter...Mr Wolowitz! | ||
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Recognizable
Netherlands1552 Posts
On April 01 2013 00:18 iamho wrote: I used to think quantum physics was awesome until I took a class on it.. Then I realized it was pretty much the standard "here's some equations someone smarter than you derived, manipulate them and do math" type of thing. Also I still have no idea what the conceptual explanation for matrices and eigenvectors are, despite acing the class. To the math purists out there, I'd say that as a non-physics major, the non-math explanations and the pop science I read were both far more engaging and useful than the equations. Don't they at least show how it was derived? I went to a class on classical mechanics and the whole class was about deriving the formulas. | ||
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micronesia
United States24775 Posts
On April 02 2013 01:06 Recognizable wrote: Don't they at least show how it was derived? I went to a class on classical mechanics and the whole class was about deriving the formulas. Well quantum mechanics can's always be derived the way classical mechanics can. For example, the Schrodinger Equation itself was proposed rather than derived. | ||
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Recognizable
Netherlands1552 Posts
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micronesia
United States24775 Posts
On April 02 2013 01:13 Recognizable wrote: How do you propose an equation on unimaginable things like these? I'm not sure how to answer this. They had a pretty good idea of what solutions the Schrodinger equation should give, and how they should behave under some simple situations, I guess. It was just a matter of finding the right differential equation. Maybe a quantum expert can weigh in more. | ||
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Teoita
Italy12246 Posts
Several phenomena such as black body radiation, the Stern-Gerlach experiment, the photoelectric effect etc were explained by hypothesizing the existence of quantum behaviour. This is known as "old" quantum physics, and had no theoretical basis. Rather, it was a collection of ad-hoc assumptions for each experiment. What Dirac, Heisenberg and Shroedinger did was provide a physical theory that explained all this behaviours. What this means is, they provided some very specific (and abstract) postulates, and then demonstrated that by using these mathematical hypothesis it was possible to model quantum behaviour, that is, to have a mathematical model that explained all these phenomena and was able to predict even more things (which essentially means, contructing a theory in the scientific sense of the word). If you want to read more, take a look at wikipedia's page, it's pretty ok: http://en.wikipedia.org/wiki/Postulate_of_quantum_mechanics | ||
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CoughingHydra
177 Posts
On April 02 2013 01:15 micronesia wrote: I'm not sure how to answer this. They had a pretty good idea of what solutions the Schrodinger equation should give, and how they should behave under some simple situations, I guess. It was just a matter of finding the right differential equation. Maybe a quantum expert can weigh in more. From what I heard (I'm only a maths student), Feynman uses in his lectures the analogous interpretation of quantum mechanics to the Lagrangian interpretation of classical mechanics. In Lagrangian mechanics, a particle's trajectory is such that the difference between kinetic and potential energy (summarized through time) is minimal. From this you can derive Newton's second law. The analogous interpretation in quantum would be that you look at all possible trajectories and each will give a certain contribution to the final wave function. From this you should be able to get the Schroedinger equation. EDIT: http://en.wikipedia.org/wiki/Quantum_mechanics#Mathematically_equivalent_formulations_of_quantum_mechanics Also, from: http://en.wikipedia.org/wiki/Schrödinger_equation Like Newton's Second law, the Schrödinger equation can be mathematically transformed into other formulations such as Werner Heisenberg's matrix mechanics, and Richard Feynman's path integral formulation | ||
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Teoita
Italy12246 Posts
Feynman's formulation of quantum mechanics (which is what you described) is from the 50's ish, it has nothing to do with how it was first written in the 30's. If you want to be technical, Shroedinger's equation is simply written H |E> = E |E>, and it's a "simple" eigenvalue/eigenvector problem. H is the hamiltonian, |E> is an eigenvector and E the corresponding eigenvalue. The messy thing of course is figuring out how to write it explicitly when you are finding the eigenvalues and eigenvectors in a spite that has infinite dimensions, and sometimes even continous dimensions (the equations in quantum mechanics are written in l2 spaces for the math students out there). That's where all the derivatives and such that you see in how it's usually written come in; those are one way to represent the operators present in the Hamiltonian. This was the approach first used by Dirac, Heisenberg and Shroedinger in the 30's. Feynman simply introduced yet another way of looking at the math framework of quantum physics, which proved extremely valuable in formulating the more "modern" quantum theories, known as quantum field theory (of which i know next to nothing because it's FUCKING COMPLEX SHIT). | ||
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micronesia
United States24775 Posts
The commutator of position and momentum is i*h_bar | ||
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Teoita
Italy12246 Posts
edit: unless you talk about crazy shit like string theory or other unified field theories. There -might- be some more general principle from which the quantization postulate comes from, but yeah, not many people would be aware of that and even less would understand wtf is written. | ||
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