The Eigenfunctions

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Fig 3: Each of the eigenvectors of H^TH (one of the the columns of V) may be mapped onto

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Fig 3: Each of the eigenvectors of H^TH (one of the the columns of V) may be mapped onto the lattice since each component of the vector is associated with a lattice point. When we do this we generate two-dimensional functions in the circular space we have chosen for the solution. These functions are (by definition) orthonormal. Because we have chosen a circular boundary, they look rather like cylinder functions. In fact they have a symmetry characteristic of the geometry of the problem.

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Fig 3: Each of the eigenvectors of H^TH (one of the the columns of V) may be mapped onto the lattice since each component of the vector is associated with a lattice point. When we do this we generate two-dimensional functions in the circular space we have chosen for the solution. These functions are (by definition) orthonormal. Because we have chosen a circular boundary, they look rather like cylinder functions. In fact they have a symmetry characteristic of the geometry of the problem.

© Kenneth C. Holmes

© Kenneth C. Holmes

Each of the eigenvectors of H^TH (one of the the columns of V) may be mapped onto the lattice since each component of the vector is associated with a lattice point. When we do this we generate two-dimensional functions in the circular space we have chosen for the solution. These functions are (by definition) orthonormal. Because we have chosen a circular boundary, they look rather like cylinder functions. In fact they have a symmetry characteristic of the geometry of the problem. Some examples from a case considered below are shown in Fig 3.