Curvature induced quantum potential on deformed surfaces

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 solve the inverse problem and show the way to derive a surface with prescribed quantum properties. We also show that there exist surfaces in the form of a circular strip around the axis of symmetry which allow particles with generic angular momentum to bind.