The theory of a quantum-mechanical particle confined to a surface of revolution is described using differential geometry methods including the derivation of a general set of three ordinary differential equations in curved coordinates. The problem is shown to be completely separable with the present hard-wall boundary conditions. Two case studies of recent experimental interest. the nanocone and torus-shaped nanoring structures. are analyzed in terms of eigenstates, energies. and symmetry characteristics based on the theory presented.
Physica Scripta, 2005, Vol 72, Issue 2-3, p. 105-111