0185352 - UJF-V 20010079 RIV GB eng J - Journal Article
Exner, Pavel - Krejčiřík, David
Bound states in mildly curved layers.
Journal of Physics. A - Mathematical and General Physics. Roč. 34, - (2001), s. 5969-5985. ISSN 0305-4470
R&D Projects: GA AV ČR KSK1010104
Subject RIV: BE - Theoretical Physics
Impact factor: 1.542, year: 2001

It has been shown recently that a nonrelativistic quantum particle constrained to a hard-wall layer of constant width built over a geodesically complete simply connected noncompact curved surface can have bound states, provided the surface is not a plane. In this paper we study the weak-coupling asymptotics of these bound states, i.e., the situation when the surface is a mildly curved plane. Under suitable assumptions about regularity and decay of surface curvatures we derive the leading order in the ground-state eigenvalue expansion. The argument is based on Birman-Schwinger analysis of Schrodinger operators in a planar hard-wall layer.
Permanent Link: http://hdl.handle.net/11104/0081751