  An analytic expression is derived for the distribution $G(\vec{R})$ of the
end-to-end distance $\vec{R}$ of semiflexible polymers in external potentials
to elucidate the effect of confinement on the mechanical and statistical
properties of biomolecules. For parabolic confinement the result is exact
whereas for realistic potentials a self-consistent ansatz is developed, so that
$G(\vec{R})$ is given explicitly even for hard wall confinement. The
theoretical result is in excellent quantitative agreement with fluorescence
microscopy data for actin filaments confined in rectangularly shaped
microchannels. This allows an unambiguous determination of persistence length
$L_P$ and the dependence of statistical properties such as Odijk's deflection
length $\lambda$ on the channel width $D$. It is shown that neglecting the
effect of confinement leads to a significant overestimation of bending
rigidities for filaments.
