Some Spectral Properties of Schrödinger Operators on Semi Axis

İbrahim Erdal

Article Details

Some Spectral Properties of Schrödinger Operators on Semi Axis

Authors:

İbrahim Erdal

Publisher:

Sakarya University

Main Topics:

Mathematical Sciences

Journal:

Sakarya University Journal of Science Vol.27 Issue 3, pp.542-549

Document Type:

Article

Publication Date:

6/2023

Document Language:

English

Document ID (Org No.):

2001292207

pISSN:

2147-835X

Keywords:

Abstract:

 The main aim of this work is to investigate some spectral properties of Schrödinger operators on semi axis. We first present the Schrödinger equation with a piecewise continuous potential function q so that the problem differs from the classical Schrödinger problems. Then, we get the Wronskian of two specific solution of the given equation which helps us to create the sets of eigenvalues and spectral singularities. The rest of the paper deals with eigenvalues and spectral singularities. By the help of the analytical properties of Jost solutions and resolvent operator of the Schrödinger operators, we provide sufficient conditions guarenteeing finiteness of eigenvalues and spectral singularities with finite multiplicities.

 The main aim of this work is to investigate some spectral properties of Schrödinger operators on semi axis. We first present the Schrödinger equation with a piecewise continuous potential function q so that the problem differs from the classical Schrödinger problems. Then, we get the Wronskian of two specific solution of the given equation which helps us to create the sets of eigenvalues and spectral singularities. The rest of the paper deals with eigenvalues and spectral singularities. By the help of the analytical properties of Jost solutions and resolvent operator of the Schrödinger operators, we provide sufficient conditions guarenteeing finiteness of eigenvalues and spectral singularities with finite multiplicities.

 The main aim of this work is to investigate some spectral properties of Schrödinger operators on semi axis. We first present the Schrödinger equation with a piecewise continuous potential function q so that the problem differs from the classical Schrödinger problems. Then, we get the Wronskian of two specific solution of the given equation which helps us to create the sets of eigenvalues and spectral singularities. The rest of the paper deals with eigenvalues and spectral singularities. By the help of the analytical properties of Jost solutions and resolvent operator of the Schrödinger operators, we provide sufficient conditions guarenteeing finiteness of eigenvalues and spectral singularities with finite multiplicities.

 The main aim of this work is to investigate some spectral properties of Schrödinger operators on semi axis. We first present the Schrödinger equation with a piecewise continuous potential function q so that the problem differs from the classical Schrödinger problems. Then, we get the Wronskian of two specific solution of the given equation which helps us to create the sets of eigenvalues and spectral singularities. The rest of the paper deals with eigenvalues and spectral singularities. By the help of the analytical properties of Jost solutions and resolvent operator of the Schrödinger operators, we provide sufficient conditions guarenteeing finiteness of eigenvalues and spectral singularities with finite multiplicities.

Article Details

Some Spectral Properties of Schrödinger Operators on Semi Axis

Authors: İbrahim Erdal

Publisher: Sakarya University

Main Topics: Mathematical Sciences

Journal: Sakarya University Journal of Science Vol.27 Issue 3, pp.542-549

Document Type: Article

Publication Date: 6/2023

Document Language: English

Document ID (Org No.): 2001292207

pISSN: 2147-835X

Schrödinger operators

eigenvalues

spectral singularities

resolvent operator

Issues

Authors:

İbrahim Erdal

Publisher:

Sakarya University

Main Topics:

Mathematical Sciences

Journal:

Sakarya University Journal of Science Vol.27 Issue 3, pp.542-549

Document Type:

Article

Publication Date:

6/2023

Document Language:

English

Document ID (Org No.):

2001292207

pISSN:

2147-835X