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I have been working on a quantum mechanics problem I asked here and someone recommended to use path integrals. I learned about path integrals but I couldn't find out how to finding the most optimized path of a quantum particle. How can I use path integrals to do so?

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TanMath
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  • This question (v1) is essentially a duplicate of this question by OP: http://physics.stackexchange.com/q/149953/2451 – Qmechanic Dec 06 '14 at 07:42
  • What do you mean by the most optimized path? If it is the path with minimal action on the path then you could use classical mechanics to find it. Otherwise you could optimize your own function using Euler-Lagrange equations. – nvvm Dec 06 '14 at 10:20
  • I saw the previous question of Abraham, and I wonder why should it have been closed. Abraham is confused, and recommending him to show effort, is to send him to no precise direction. One could have asked him WHY HAS the particle to go through the shortest path, and toward which point/region/device/etc. Here is a reference fit for him: Gordon Baym, "Lectures on Quantum Mechanics", chapter 3, "Motion of particles in Quantum Mechanics", section "Quantum mechanical motion as a sum over paths". This book is excellent for beginners, it is very intuitive. – Sofia Dec 06 '14 at 12:38
  • (continuation) Please don't feel upset with my comment. In your early years of studying quantum mechanics, you never were confused? – Sofia Dec 06 '14 at 12:46
  • @Qmechanic um.. that's my question! – TanMath Dec 06 '14 at 19:01
  • @nvvm but if the particle is in the quantum scale, I still use classical mechanics? What do you mean by using the Euler Lagrange equations? How would I use that? – TanMath Dec 06 '14 at 19:02
  • @sofia i would like to learn with online and free resources, if possible... – TanMath Dec 06 '14 at 20:11
  • @Abraham: which Euler angles? What for? You go to this address in Internet, http://www.amazon.com/Lectures-Quantum-Mechanics-Lecture-Supplements/dp/0805306676/ref=sr_1_1?ie=UTF8&s=books&qid=1245448296&sr=1-1 They say that it's free two day shipping for college students. Another possibility, here is his email, gbaym@illinois.edu , write him, tell him that you cannot pay and need urgently, and ask him to send you. DON'T BE SHY ! – Sofia Dec 07 '14 at 02:07
  • @TAbraham in quantum mechanics there is no "path of a particle". Instead there is a continuum of paths (in path integral formulation) and particle realize all of them. But if you want to select the most optimized path from the continuum of paths you should use classical mechanics to find it. It will be not the actual path of the particle but the most optimized of possible paths. – nvvm Dec 07 '14 at 19:52
  • @nvvm What I want is that the optimized path of a particle should have the highest probability amplitude... Does that make more sense? – TanMath Dec 07 '14 at 19:55
  • Amplitude of each path is $\text{const}\cdot e^{i\frac S \hbar}$, so probability of each of them is equal. – nvvm Dec 07 '14 at 20:15
  • @nvvm then there is no way for us to increase the probability amplitude for certain paths? Then what about decoherence? – TanMath Dec 07 '14 at 20:28
  • @nvvm so it is not possible to do this problem? – TanMath Dec 14 '14 at 22:41

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