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Shankar Exercise 2.5.1 - Hamiltonion

by ehrenfest
Tags: hamiltonian
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ehrenfest
#1
Jun18-07, 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
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malawi_glenn
#2
Jun19-07, 01:40 AM
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http://www.physicsforums.com/showthread.php?t=8997
dextercioby
#3
Jun19-07, 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.

CompuChip
#4
Jun19-07, 02:17 PM
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Shankar Exercise 2.5.1 - Hamiltonion

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]
ehrenfest
#5
Jun19-07, 07:59 PM
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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].
malawi_glenn
#6
Jun20-07, 12:34 AM
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And was does the rest stand for?

Work done so far? etc.
ehrenfest
#7
Jun20-07, 02:59 PM
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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.
ehrenfest
#8
Jun21-07, 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.
dextercioby
#9
Jun23-07, 10:51 AM
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Quote Quote by ehrenfest View Post
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].
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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