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Quantum-mechanics on graphs

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<mark>Journal publication date</mark>21/10/1994
<mark>Journal</mark>Journal of Physics -London- a Mathematical and General
Issue number20
Number of pages12
Pages (from-to)6881-6892
<mark>Original language</mark>English


We analyse the problem of one-dimensional quantum mechanics on arbitrary graphs as idealized models for quantum systems on spaces with non-trivial topologies. In particular we argue that such models can be made to accommodate the physical characteristics of wavefunctions on a network of wires and offer several derivations of a particular junction condition. Throughout we adopt a continuity condition for the wavefunction at each primitive node in the network. Results are applied to the problem of the energy spectrum of a system containing one and infinitely many junctions.