| March 16, 2007 17:18 WSPC/INSTRUCTION FILE vertapp Reviews in Mathematical Physics c ○ World Scientific Publishing Company Approximations of singular vertex couplings in quantum graphs (2008) | |||||||||||||||||
Abstract | |||||||||||||||||
| Revised (Day Month Year) We discuss approximations of the vertex coupling on a star-shaped quantum graph of n edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation symmetry is present. It is shown that the Cheon-Shigehara technique using δ interactions with nonlinearly scaled couplings yields a 2n-parameter family of boundary conditions in the sense of norm resolvent topology. Moreover, using graphs with additional edges one can approximate the n+1 2¡-parameter family of all time-reversal invariant couplings. | |||||||||||||||||
Publication details | |||||||||||||||||
| |||||||||||||||||