# Shankar Exercise 2.5.1 - Hamiltonion

1. Jun 18, 2007

### 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

2. Jun 19, 2007

### malawi_glenn

3. Jun 19, 2007

### dextercioby

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

4. Jun 19, 2007

### CompuChip

Ad 2: Yes, use the [ tex] tag (without the space):
$$\left[-\frac{\hbar^2}{2 m} \nabla^2 + U(\mathbf{r}) \right] \psi (\mathbf{r}) = E \psi (\mathbf{r}).$$

5. Jun 19, 2007

### ehrenfest

Show that if $$T = \sum_i\sum_jT_ij(q)q_i' q_j'$$, where $$q_i'$$'s are generalized velocities, then $$\sum p_i q_i' = 2T$$.

6. Jun 20, 2007

### malawi_glenn

And was does the rest stand for?

Work done so far? etc.

7. Jun 20, 2007

### 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.

8. Jun 21, 2007

### 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.

9. Jun 23, 2007

### dextercioby

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