scholarly journals Some properties on extended eigenvalues and extended eigenvectors

2019 ◽  
Vol 24 (6) ◽  
pp. 128
Author(s):  
Laith K. Shaakir1 ◽  
Anas A. Hijab2
Keyword(s):  
Shift Operator ◽  
Unilateral Shift

In this paper, the study extended eigenvalues and extended eigenvectors, and we will investigate the  and give for some concepts properties and result important, also we will find the  and  on the  space, so U is Unilateral shift operator and .   http://dx.doi.org/10.25130/tjps.24.2019.119

scholarly journals On unilateral shift operators and C0-operators

1992 ◽  
Vol 53 (1) ◽  
pp. 137-142
Author(s):  
Il Bong Jung ◽  
Yong Chan Kim
Keyword(s):  
Hilbert Space ◽  
Shift Operator ◽  
Matrix Form ◽  
Operator Matrix ◽  
Unilateral Shift ◽  
Shift Operators

AbstractLet S(n) be a unilateral shift operator on a Hilbert space of multiplicity n. In this paper, we prove a generalization of the theorem that if S(1) is unitarily equivalent to an operator matrix form relative to a decomposition ℳ ⊕ N, then E is in a certain class C0 which will be defined below.

scholarly journals SUSUSY Quantum Mechanics

1997 ◽  
Vol 12 (01) ◽  
pp. 171-176 ◽  
Author(s):  
David J. Fernández C.
Keyword(s):  
Quantum Mechanics ◽  
Shift Operator ◽  
Second Order ◽  
Parametric Family ◽  
First Order ◽  
Shift Operators ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

The exactly solvable eigenproblems in Schrödinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham–Moses potentials as a particular case.

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