  In this paper, we study the spectrum of quantum tubes. Under certain
intrinsic assumptions of the asymptotically flat submanifold of the Euclidean
space, we prove the existence of the ground state of the quantum tube. The work
is a generalization of Duclos, Exner and Krejcirik (CMP, 223(1), 13-28, 2001)
and ourselves(math.DG/0402252).
