# Hamiltonian

by ehrenfest
Tags: hamiltonian
 P: 1,998 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
 HW Helper Sci Advisor P: 4,739
 HW Helper Sci Advisor P: 11,720 Post the text of the problem for those of us who don't have the book, but might be willing to help you.
HW Helper
P: 4,281

## Hamiltonian

Ad 2: Yes, use the [ tex] tag (without the space):
$$\left[-\frac{\hbar^2}{2 m} \nabla^2 + U(\mathbf{r}) \right] \psi (\mathbf{r}) = E \psi (\mathbf{r}).$$
 P: 1,998 Show that if $$T = \sum_i\sum_jT_ij(q)q_i' q_j'$$, where $$q_i'$$'s are generalized velocities, then $$\sum p_i q_i' = 2T$$.
 HW Helper Sci Advisor P: 4,739 And was does the rest stand for? Work done so far? etc.
 P: 1,998 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.
 P: 1,998 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.
HW Helper
 Quote by ehrenfest Show that if $$T = \sum_i\sum_jT_ij(q)q_i' q_j'$$, where $$q_i'$$'s are generalized velocities, then $$\sum p_i q_i' = 2T$$.
Since $p_{i}=\frac{\partial L}{\partial q^{i}}$, i gues the result is pretty obvious, don't you think ?