Identities for Eigenvalues of the Schrödinger Equation with Energy-Dependent Potential

Yang, Caiqin

doi:10.5560/zna.2011-0023

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“…With the method of asymptotic estimation on the family of contours [17], Cao and Zhuang [18] studied regularized traces of the Schrödinger equation with energy-dependent potential, in which the final quantity only contains the term with P(x). Further, Yang [19][20][21] obtained some new formulae related to both P(x) and Q(x).…”

Section: Introductionmentioning

confidence: 99%

Trace Formulae for Second-Order Differential Pencils with a Frozen Argument

Hu,

Şat

2023

Mathematics

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This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, the trace formulae have the same form which reveals the impact of the frozen argument.

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