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Hamiltonianby ehrenfest
Tags: hamiltonian 
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#1
Jun1807, 11:00 PM

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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
Jun1907, 01:40 AM

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#3
Jun1907, 12:26 PM

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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.



#4
Jun1907, 02:17 PM

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Hamiltonian
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] 


#5
Jun1907, 07:59 PM

P: 1,996

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].



#6
Jun2007, 12:34 AM

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And was does the rest stand for?
Work done so far? etc. 


#7
Jun2007, 02:59 PM

P: 1,996

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. 


#8
Jun2107, 02:49 AM

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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.



#9
Jun2307, 10:51 AM

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