March 3, 2026Open Access

Uniqueness for the Schrödinger equation on graphs with potential vanishing at infinity

Key Points

Uniqueness is established for solutions to the Schrödinger equation on infinite graphs with controlled vanishing potentials.
Key findings demonstrate that these solutions remain valid even when the potential is not bounded away from zero.
Assessment of uniqueness in suitable weighted ℓ p spaces offers new insights into previously established results.
Findings may enable a richer understanding of quantum behaviors in more complex graph structures.

Abstract

Abstract We study the uniqueness of solutions to the stationary Schrödinger equation with potential on infinite graphs, within suitable weighted ᵖ ℓ p spaces. The potential is allowed to vanish at infinity at a controlled rate. Our results extend those in 20 by considering a broader class of potentials, by removing the assumption that the potential is bounded away from zero.

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Discussion

Authors

Fabio Punzo

Marcello Svagna

Journals

Nonlinear Differential Equations and Applications NoDEA

Actions

Institutions

Politecnico di Milano

References and Citations

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Building similarity graph...

Analyzing shared references across papers

Uniqueness for the Schrödinger equation on graphs with potential vanishing at infinity

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

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