  We present a detailed study of the finite one-dimensional quantum Ising chain
in a transverse field in the presence of boundary magnetic fields coupled with
the order-parameter spin operator. We consider two magnetic fields located at
the boundaries of the chain that have the same strength and that are aligned in
the same or in the opposite direction. We derive analytic expressions for the
gap in all phases for large values of the chain length L, as a function of the
boundary field strength. We also investigate the behavior of the chain in the
quantum ferromagnetic phase for oppositely aligned fields, focusing on the
magnet-to-kink transition that occurs at a finite value of the magnetic field
strength. At this transition we compute analytically the finite-size crossover
functions for the gap, the magnetization profile, the two-point correlation
function, and the density of fermionic modes. As the magnet-to-kink transition
is equivalent to the wetting transition in two-dimensional classical Ising
models, our results provide new analytic predictions for the finite-size
behavior of Ising systems in a strip geometry at this transition.
