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Note on the numerical solution of the scalar Helmholtz equation in a nanotorus with uniform Dirichlet boundary conditions

This note describes the solution of the Helmholtz equation inside a nanotorus with uniform Dirichlet boundary conditions. The eigenfunction symmetry is discussed and the lower-order eigenvalues and eigenfunctions are shown. The similarity with the case of a long cylinder and with that of the vibrations of a circular elastic membrane is discussed. This similarity is used to propose a classification scheme of the eigenfunctions based on three indices.