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Using the principle of conservation of energy

  1. Oct 10, 2014 #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
     
  2. jcsd
  3. Oct 11, 2014 #2

    vela

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    Let's be honest. It's not too long; you're just too lazy to type it in.
     
  4. Oct 11, 2014 #3
    Ok fair enough! I'm using u phone so I find it much better to post photographs
     
  5. Oct 11, 2014 #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 ?
     
  6. Oct 11, 2014 #5
    So potential between that a and 0 is not 0?
     
  7. Oct 11, 2014 #6
    I'm not sure I follow what you are saying?
     
  8. Oct 11, 2014 #7

    vela

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    He's saying there's a mistake in the fifth line of your work.
     
  9. Oct 11, 2014 #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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