Quantum-mechanics on graphs

GRATUS, J and Lambert, Colin and Robinson, Simon and Tucker, Robin (1994) Quantum-mechanics on graphs. Journal of Physics A: Mathematical and General, 27 (20). pp. 6881-6892. ISSN 0305-4470

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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.

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Journal Article
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Journal of Physics A: Mathematical and General
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10 Jan 2012 11:41
Last Modified:
16 Sep 2023 00:39