  We investigate the effect of curvature on the behaviour of a quantum particle
bound to move on a surface. For the Gaussian bump we derive and discuss the
quantum potential which results in the appearance of a bound state for
particles with vanishing angular momentum. The Gaussian bump provides a
characteristic length for the problem. For completeness we propose an inverse
problem in differential geometry, i.e. what deformed surfaces produce
prescribed curvature induced quantum potentials. We solve this inverse problem
in the case of rotational surfaces. We also show that there exist rotational
surfaces in the form of a circular strip around the axis of symmetry which
allow particles with generic angular momentum to bind.
