  We elucidate the elastic behavior of a wormlike chain in 3D under compression
and provide exact solutions for the experimentally accessible force-extension
relation in terms of generalized spheroidal wave functions. In striking
contrast to the classical Euler buckling instability, the force-extension
relation of a clamped semiflexible polymer exhibits a smooth crossover from an
almost stretched to a buckled configuration. In particular, the associated
susceptibility, which measures the strength of the response of the polymer to
the applied force, displays a prominent peak in the vicinity of the critical
Euler buckling force. For increasing persistence length, the force-extension
relation and the susceptibility of semiflexible polymers approach the behavior
of a classical rod, whereas thermal fluctuations permit more flexible polymers
to resist the applied force. Furthermore, we find that semiflexible polymers
confined to 2D can oppose the applied force more strongly than in 3D.
