\magnification=\magstep1

$$
\Delta E \thinspace \Delta t \quad \simeq \quad \hbar
$$






$$
\Delta E \Delta t \simeq {\hbar} 
$$

$$
{{\Delta \lambda}\over{\lambda_0}} \quad = \quad \sqrt{ {{1 - (v/c)}\over{1 + (v/c)}} }
$$

$$
{{\Delta \lambda}\over{\lambda_0}} \quad \simeq \quad {{v}\over{c}}
$$

$$
{\rm mean\ free\ path\ \ } \ell \quad  = \quad {{1}\over{n \sigma}}
$$

$$
v_{\rm thermal} \quad = \quad \sqrt{{2 k T}\over{m}}
$$

$$
\Delta t \quad = \quad {{\ell}\over{v_{\rm thermal}}}
  \quad = \quad 
          {{1}\over{n \sigma }} \ \sqrt{{m}\over{2kT}}
$$



\bye
