Quantum mechanics

Quantum graph

Pure mathematics

Boundary value problem

Vertex (graph theory)

Scattering

Astrophysics

Statistical physics

Physics

Graph

Mathematics

Spectral properties

Condensed matter physics

Mathematical analysis

Geometry

Quantum

Connection (principal bundle)

Combinatorics

Topology (electrical circuits)

Journal of the Physical Society of Japan

We examine scattering properties of singular vertex of degree $n=2$ and $n=3$, taking advantage of a new form of representing the vertex boundary condition, which has been devised to approximate a singular vertex with finite potentials. We show that proper identification of $δ$ and $δ'$ components in the connection condition between outgoing lines enables the designing of quantum spectral branch-filters.

Spectral Filtering in Quantum Y-Junction