Singularities of the green function of the nonstationary Schrödinger equation

1998 ◽  
Vol 32 (2) ◽  
pp. 132-134
Author(s):  
M. V. Buslaeva ◽  
V. S. Buslaev
Keyword(s):  
Green Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonstationary Schrödinger Equation ◽  
The Green Function

Fractional Schrödinger equation and anomalous relaxation: Nonlocal terms and delta potentials

2021 ◽  
pp. 2140004
Author(s):  
Ervin K. Lenzi ◽  
Luiz R. Evangelista ◽  
Rafael S. Zola ◽  
Irina Petreska ◽  
Trifce Sandev
Keyword(s):  
Green Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fractional Schrödinger Equation ◽  
Anomalous Relaxation ◽  
Delta Functions ◽  
The Green Function ◽  
Nonlocal Terms ◽  
Green Function Approach ◽  
Fractional Schrodinger Equation

We review and extend some results for the fractional Schrödinger equation by considering nonlocal terms or potential given in terms of delta functions. For each case, we have obtained the solution in terms of the Green function approach.

PERTURBED SCHRÖDINGER EQUATION WITH SINGULAR POTENTIAL AND INITIAL DATA

2006 ◽  
Vol 08 (04) ◽  
pp. 433-452 ◽  
Author(s):  
MIRJANA STOJANOVIĆ
Keyword(s):  
Initial Data ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Singular Potential ◽  
Singular Integral Equations ◽  
Uniqueness Result ◽  
Stability Estimates ◽  
Delta Distribution ◽  
The Green Function ◽  
Regularized Derivatives

We consider linear Schrödinger equation perturbed by delta distribution with singular potential and the initial data. Due to the singularities appearing in the equation, we introduce two kinds of approximations: the parameter's approximation for potential and the initial data given by mollifiers of different growth and the approximation for the Green function for Schrödinger equation with regularized derivatives. These approximations reduce the perturbed Schrödinger equation to the family of singular integral equations. We prove the existence-uniqueness theorems in Colombeau space [Formula: see text], 1 ≤ p,q ≤ ∞, employing novel stability estimates (w.r.) to singular perturbations for ε → 0, which imply the statements in the framework of Colombeau generalized functions. In particular, we prove the existence-uniqueness result in [Formula: see text] and [Formula: see text] algebra of Colombeau.

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