Timeline for A novice question on Quantum Mechanics
Current License: CC BY-SA 3.0
7 events
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| Dec 27, 2012 at 0:31 | comment | added | Vectornaut | @IgorKhavkine -- Yes, the linearity of the Schrödinger equation is very important from a technical standpoint: as you alluded, it allows you to use things like Green's functions and partial waves for solving scattering problems, and the discrete Fourier transform for designing quantum algorithms. For me, however, the word "superposition" is loaded with conceptual baggage, and brings to mind lots of unhelpful talk about photons going through two slits at once and cats being alive and dead at the same time. I don't understand why state vector addition is assigned such conceptual importance. | |
| Dec 26, 2012 at 6:05 | comment | added | Igor Khavkine | Summing state vectors is definitely different from summing density operators. Both are important in their own ways. To appreciate the important of superposition of state vectors, one need only open any physics textbook of quantum mechanics. What underlies the importance of superpositions is the Born rule (inner products -> probabilities) which includes in it quantum interference effects. Such effects show up notoriously for particles interacting with barriers or slits, entangled photons in EPR states, non-trivial quantum computer algorithms. Hard to overstate the importance of superposition. | |
| Dec 26, 2012 at 5:28 | comment | added | Vectornaut | @ChrisGerig -- (3) Just to be clear, I do think that taking convex combinations of density operators is an extremely useful and conceptually important operation. But, as far as I know, summing state vectors has nothing to do with summing the corresponding density operators. Am I mistaken? | |
| Dec 26, 2012 at 5:24 | comment | added | Vectornaut | @ChrisGerig -- (1) I'd like to understand why you find the idea of superposition important, since I've never been able to get much use out of it. Can you give an example of a situation where you find it particularly useful, or maybe an explanation of why you think it's "the whole point"? (2) Maybe your "B = C - A" comment is a good place to start looking for the disconnect between our points of view. When I read it, my first thought was, "I don't see why it's useful to think of the number 4 as a superposition of the numbers -11 and 7." Am I missing the point somehow? | |
| Dec 25, 2012 at 8:57 | comment | added | Chris Gerig | As to your photon-polarizer example, I believe it is misleading: Superposition still works, it was just hidden. $|H\rangle$ is a superposition of $|L\rangle$ and $|R\rangle$, and now your two states mix. It's like if I took $A+B$ but forgot to tell you that $B=C-A$. | |
| Dec 25, 2012 at 8:46 | comment | added | Chris Gerig | This is just a vamped version of my post. And I completely disagree about "forgetting superposition entirely"... the whole point of these states is probability and superposition. We are trying to understand how to observe the world, and quantum measurements are precisely this. | |
| Dec 25, 2012 at 8:24 | history | answered | Vectornaut | CC BY-SA 3.0 |