Quantum graphs featuring unusual self-adjoint extensions
DOI:
https://doi.org/10.14311/AP.2025.65.0539Keywords:
quantum graphs, self-adjoint extensions, discrete spectrumAbstract
We present an example of a simple quantum graph with “vertices at infinity”, which appear due a strongly attractive potential making the spectral problem quantum-mechanically incomplete. We construct the appropriate self-adjoint extensions of the formal graph Hamiltonian, and derive their spectral properties.
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Copyright (c) 2025 Pavel Exner
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