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I've just started reading Feynman and Hibbs path integrals and Quantum mechanics after a decade hiatus from my undergraduate math degree (including a few semesters of physics for engineers). It would be tremendously helpful to see the step by step solutions to some of the first set of problems (Page 27-28, #2.1 and on) As many as folks are willing to post! Or if anyone knows of the solutions being available on-line that would also be helpful.

The specific concept question is finding the extremum of functional that is the integral of the lagrangian of a system (classical action). The easiest example is 2.1, show that for $L=m/2 (dx/dt)^2$, the extremum is $m/2*(x_b-x_a)^2/(t_b-t_a)$. I have tried manipulating the integral by replacing 'partial of $L$ with respect to $x$' with '$d/dt$ (partial $L$ with respect to $dx/dt$) but haven't gotten there. I know it's the easiest problem but I think if I see an example, I will be able to apply what I learn to the harder subsequent problems

I hope that's enough to come off "hold" Thanks!

Tachyon209
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user40187
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  • Related: https://physics.stackexchange.com/q/10325/2451 , https://physics.stackexchange.com/q/328439/2451 and links therein. – Qmechanic Feb 08 '14 at 09:13
  • If you write down some of your work, or specify an approach, or explain where you're stuck, then I may be able to help you. I am familiar with the book. – user35033 Feb 09 '14 at 07:55
  • Hello - I found this website: http://www2.ph.ed.ac.uk/~bjp/qt/qt.pdf It shows that you use the relationship partial of L with respect to x =d/dt (partial L with respect to dx/dt) to show that d2x/dx2 = zero, so dx/dt is constant.Therefore the integral of 1/2mv2 dt is 1/2 mv2 (ta-tb) where v is delta x over delta t. Thats the solution! I think thats all there is too it! simple..oy!If there's another nuance you'd like to highlight, please feel free! I will be working on the other problems Friday (taking day off from work to read physics!)I'll post any qs. tx user35033! – user40187 Feb 13 '14 at 06:04
  • Hi! I followed your link and found it very helpful. Just wanted to thank you for the hint. I was reading through the book myself as an amateur and had some difficulties. The lecture notes that you have suggested are quite good. Thanks (and please forgive my poor english...) – Tere_TX Jan 03 '23 at 13:06

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