On integral representation of thetranslation operator

On integral representation of thetranslation operator

The formulation in the explicit form of quantum expression of the one-dimensional translation operator as well as Hermitian operator of momentum and its eigenfunctions are presented. The interrelation between the momentum and the wave number has been generalized for the processes with a non-integer...

Full description

Bibliographic Details
Main Author: Paulius Miškinis
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2012-02-01
Series:Mathematical Modelling and Analysis
Subjects:
traslation operator
quantum mechanics
fractional calculus
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/4837
id doaj-36cbfd50545c4477aad5207bfd289a28
record_format Article
spelling doaj-36cbfd50545c4477aad5207bfd289a282021-07-02T12:34:52ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102012-02-0117110.3846/13926292.2012.645251On integral representation of thetranslation operatorPaulius Miškinis0Facult y of Funda me nt al Sciences, Vilnius Gediminas Techni cal University Saulėtekio al. 11, LT- 10223 Vilnius, Lithuania The formulation in the explicit form of quantum expression of the one-dimensional translation operator as well as Hermitian operator of momentum and its eigenfunctions are presented. The interrelation between the momentum and the wave number has been generalized for the processes with a non-integer dimensionality α. The proof of the fractional representation of the translation operator is considered. Some aspects of the translations in graduate spaces and their integral representation, as well as applications in physics are discussed. The integral representation of the translation operator is proposed. https://journals.vgtu.lt/index.php/MMA/article/view/4837traslation operatorquantum mechanicsfractional calculus
collection DOAJ
language English
format Article
sources DOAJ
author Paulius Miškinis
spellingShingle Paulius Miškinis
On integral representation of thetranslation operator
Mathematical Modelling and Analysis
traslation operator
quantum mechanics
fractional calculus
author_facet Paulius Miškinis
author_sort Paulius Miškinis
title On integral representation of thetranslation operator
title_short On integral representation of thetranslation operator
title_full On integral representation of thetranslation operator
title_fullStr On integral representation of thetranslation operator
title_full_unstemmed On integral representation of thetranslation operator
title_sort on integral representation of thetranslation operator
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2012-02-01
description The formulation in the explicit form of quantum expression of the one-dimensional translation operator as well as Hermitian operator of momentum and its eigenfunctions are presented. The interrelation between the momentum and the wave number has been generalized for the processes with a non-integer dimensionality α. The proof of the fractional representation of the translation operator is considered. Some aspects of the translations in graduate spaces and their integral representation, as well as applications in physics are discussed. The integral representation of the translation operator is proposed.
topic traslation operator
quantum mechanics
fractional calculus
url https://journals.vgtu.lt/index.php/MMA/article/view/4837
work_keys_str_mv AT pauliusmiskinis onintegralrepresentationofthetranslationoperator
_version_ 1721330007404445696

Similar Items