Integration/ boundary conditions

1. Apr 4, 2013

Abigale

Hi guys,

I regard a particle in an Potential.

I have callculated the partition function and the probability density function $F_{1}$.

$$H= \frac{p^{2}_{x}}{2m} + \frac{p^{2}_{z}}{2m}+ \frac{p^{2}_{\phi}}{2I}+ mgz$$

For callculating an average value I do:
$$<mgz>=\int \limits_{\color{Brown}?}^{\color{Brown}?}dx\int \limits_{\color{Brown}?}^{\color{blue}+ \color{blue}\infty}dz\int \limits_{\color{Brown}?}^{\color{Brown}?}d\phi~~~\int \limits_{-\infty}^{+\infty}dp_{x}\int \limits_{-\infty}^{+\infty}dp_{z}\int \limits_{-\infty}^{+\infty}dp_{\phi} ~ ~~~~F_{1} ~mgz$$

The boundary conditions are:
$$0 \le x \le L \\ 0 \le z \le {\color{blue} + \color{blue}\infty}\\ 0\le \phi \le 2\pi \\$$

Do I have to integrate to $+/- \infty$ or to the boundary conditions?

Thanks a lot
Abby