Gratus, J.; Lambert, C. J.; Robinson, S. J.; Tucker, R. W. Quantum mechanics on graphs. (English) Zbl 0858.47041 J. Phys. A, Math. Gen. 27, No. 20, 6881-6892 (1994). Summary: 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. Cited in 3 Documents MSC: 47N50 Applications of operator theory in the physical sciences 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis Keywords:one-dimensional quantum mechanics on arbitrary graphs; physical characteristics of wavefunctions on a network of wires PDFBibTeX XMLCite \textit{J. Gratus} et al., J. Phys. A, Math. Gen. 27, No. 20, 6881--6892 (1994; Zbl 0858.47041) Full Text: DOI Link