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Integration/ boundary conditions

  1. Apr 4, 2013 #1
    Hi guys,

    I regard a particle in an Potential.

    I have callculated the partition function and the probability density function [itex]F_{1}[/itex].

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

    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 [itex]+/- \infty[/itex] or to the boundary conditions?

    Thanks a lot
    Abby
    :approve:
     
  2. jcsd
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