Abstract
The low-energy excitation spectrum of an Ising quantum chain in a transverse field which is critical (h=J=1) for 1-1). Interface critical exponents are determined numerically in the odd sector and exactly in the even sector using finite-size scaling. One gets an ordinary surface transition when h)J and an extraordinary surface transition when h(J. The gap-exponent relation is verified, the mass gaps and the level degeneracy are in agreement with conformal invariance.