Hamiltonian

ehrenfest

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

malawi_glenn

http://www.physicsforums.com/showthread.php?t=8997

dextercioby

Post the text of the problem for those of us who don't have the book, but might be willing to help you.

CompuChip

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

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

And was does the rest stand for?

Work done so far? etc.

ehrenfest

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

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

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