The Zeta Function for the Triangular Potential
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Publication:6416849
DOI10.1063/5.0071099arXiv2211.05808MaRDI QIDQ6416849
Publication date: 10 November 2022
Abstract: The zeta functions for the Schr"odinger equation with a triangular potential are investigated. Values of the zeta functions are computed using both the Weierstrass factorization theorem and analytic continuation via contour integration. The results were found to be consistent where the domains of the two methods overlap. Analytic continuation is used to compute values of the zeta functions at zero and the negative integers, explore the pole structure (and residue values), as well as the value of the slopes at the origin. Those results are used for the computation of the trace and determinant of the associated Hamiltonians.
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Hamilton's equations (70H05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Other Dirichlet series and zeta functions (11M41)
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