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Quantum-mechanics on graphs

Research output: Contribution to journalJournal article

Published

Journal publication date21/10/1994
JournalJournal of Physics -London- a Mathematical and General
Journal number20
Volume27
Number of pages12
Pages6881-6892
Original languageEnglish

Abstract

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.