Spectral determinants and zeta functions of Schrödinger operators on metric graphs

Details Spectral determinants and zeta functions of Schrödinger operators on metric graphs Spectral determinants and zeta functions of Schrödinger operators on metric graphs

2011-11-02

arxiv.org/abs/1111.0643v2

Physics

Mathematical Physics

16 pages, 2 figures

Scientific paper

A derivation of the spectral determinant of the Schr\"odinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader. To formulate the spectral determinant we first derive the spectral zeta function of the Schr\"odinger operator using an appropriate secular equation. The result obtained for the spectral determinant is along the lines of the recent conjecture.

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