Asymptotic behavior of the spectral function of the Schrödinger operator near a plane part of the boundary

1966 ◽  
pp. 109-138
Author(s):  
M. G. Gasymov ◽  
B. M. Levitan
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Function ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Plane Part

scholarly journals Asymptotic behavior of generalized eigenvalues of the schrodinger operator

2014 ◽  
Author(s):  
А.Б. Шабат ◽  
О.Ю. Веремеенко ◽  
М.Ш. Бадахов
Keyword(s):  
Asymptotic Behavior ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Generalized Eigenvalues

Рассматривается оператор Шредингера на прямой с финитным потенциалом. Для ряда примеров δ-образных потенциалов установлена асимптотика комплексных полюсов коэффициента прохождения 1/a(k). Планируется использовать эти полюса для построения эффективных приближенных методов решения одномерной обратной задачи рассеяния.

The Agmon spectral function for molecular hamiltonians with symmetry restrictions

1993 ◽  
Vol 440 (1910) ◽  
pp. 621-638 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Spectral Function ◽  
Schrödinger Operator ◽  
Spectral Properties ◽  
Bound States ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Polyatomic Systems

In this paper we introduce symmetry considerations into our earlier work, which was concerned with geometric spectral properties of Schrödinger operators including the N -body operators of quantum mechanics. The point of emphasis is a function introduced by Shmuel Agmon which we have named the Agmon spectral function. We show that this function is symmetric for an N -body Schrödinger operator restricted to a subspace of prescribed symmetry. We then show how it can be used to obtain criteria for the finiteness and infiniteness of bound states of polyatomic systems.

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