A remark on Krein's resolvent formula and boundary conditions
Sergio Albeverio, Konstantin Pankrashkin
TL;DR
This paper presents an analog of Krein's resolvent formula that relates resolvents of self-adjoint extensions to boundary conditions, with applications to quantum graphs and point interactions.
Contribution
It introduces a new form of Krein's resolvent formula connecting boundary conditions to self-adjoint extensions.
Findings
Derived an analog of Krein's resolvent formula.
Applied the formula to quantum graphs.
Discussed implications for systems with point interactions.
Abstract
We prove an analog of Krein's resolvent formula expressing the resolvents of self-adjoint extensions in terms of boundary conditions. Applications to quantum graphs and systems with point interactions are discussed.
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