Using the principle of conservation of energy

  • #1
Hi all,

I'm not 100% sure this belongs in this topic but it was a problem I was given in a quantum mechanics lecture so here goes, sorry if I am wrong.


Anyway I was given a hamiltonian H= T+V


Where T is kinetic energy and av is potential, and asked to use

dH/dt= 0

to find an analogy between it and Newtons laws, now my work is far to long to post using the usual method so I have attached a photograph of all my work I hope it is clear what I have done, I just want to know if this is the correct approach or I have somehow magically confused myself into what seems to be a reasonable answer :)


ImageUploadedByPhysics Forums1412978714.668321.jpg





Thanks for any help
 

Answers and Replies

  • #2
vela
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now my work is far to long to post using the usual method so I have attached a photograph of all my work
Let's be honest. It's not too long; you're just too lazy to type it in.
 
  • #3
Ok fair enough! I'm using u phone so I find it much better to post photographs
 
  • #4
BvU
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V = V(x) so ##{\partial V\over \partial t} = 0##. However, that's not what you have in your relevant equation. From that (and from any first-grader dimensional analysis) you want ##{\partial V\over \partial x}## there. Coming close to Newton already ?
 
  • #7
vela
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He's saying there's a mistake in the fifth line of your work.
 
  • #8
Ah I see it! I have


dV(x)/dt

Rather than what I should have which is

dV(x)/dx
 

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