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Shankar Exercise 2.5.1 - Hamiltonion

  1. Jun 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Could someone get me started with Exercise 2.5.1 in Shankar's Principles of Quantum Mechanics?
    Does this forum support TeX or LaTeX?


    2. Relevant equations




    3. The attempt at a solution
     
  2. jcsd
  3. Jun 19, 2007 #2

    malawi_glenn

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  4. Jun 19, 2007 #3

    dextercioby

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    Post the text of the problem for those of us who don't have the book, but might be willing to help you.
     
  5. Jun 19, 2007 #4

    CompuChip

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    Ad 2: Yes, use the [ tex] tag (without the space):
    [tex] \left[-\frac{\hbar^2}{2 m} \nabla^2 + U(\mathbf{r}) \right] \psi (\mathbf{r}) = E \psi (\mathbf{r}). [/tex]
     
  6. Jun 19, 2007 #5
    Show that if [tex] T = \sum_i\sum_jT_ij(q)q_i' q_j' [/tex], where [tex]q_i'[/tex]'s are generalized velocities, then [tex]\sum p_i q_i' = 2T [/tex].
     
  7. Jun 20, 2007 #6

    malawi_glenn

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    And was does the rest stand for?

    Work done so far? etc.
     
  8. Jun 20, 2007 #7
    T is kinetic energy and pi is the canonical momentum conjugate. Also, the apostrophes are derivatives. Sorry.

    There is not much work done so far. I wanted someone to give me a hint or just get me started.
     
  9. Jun 21, 2007 #8
    By the way, does anyone have Shankar's book? For a lot of his exercises you really need the context, so I want to know if I should keep posting questions from his book.
     
  10. Jun 23, 2007 #9

    dextercioby

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    Since [itex] p_{i}=\frac{\partial L}{\partial q^{i}} [/itex], i gues the result is pretty obvious, don't you think ?
     
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