  We present the statistical-mechanical theory of semiflexible polymers based
on the connection between the Kratky-Porod model and the quantum rigid rotator
in an external homogeneous field, and treatment of the latter using the quantum
mechanical propagator method. The expressions and relations existing for
flexible polymers can be generalized to semiflexible ones, if one replaces the
Fourier-Laplace transform of the end-to-end polymer distance, $1/(k^{2}/3+p)$,
through the matrix $\tilde{P}(k,p)=(I+ikDM)^{-1}D$, where $D$ and $M$ are
related to the spectrum of the quantum rigid rotator, and considers an
appropriate matrix element of the expression under consideration. The present
work provides also the framework to study polymers in external fields, and
problems including the tangents of semiflexible polymers. We study the
structure factor of the polymer, the transversal fluctuations of a free end of
the polymer with fixed tangent of another end, and the localization of a
semiflexible polymer onto an interface. We obtain the partition function of a
semiflexible polymer in half space with Dirichlet boundary condition in terms
of the end-to-end distribution function of the free semiflexible polymer, study
the behaviour of a semiflexible polymer in the vicinity of a surface, and
adsorption onto a surface.
