Open AccessON INTEGRAL REPRESENTATION OF THETRANSLATION OPERATOR
Author(s) -
Paulius Miškinis
Publication year - 2012
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2012.645251
Subject(s) - operator (biology) , momentum operator , mathematics , displacement operator , representation (politics) , eigenfunction , translation (biology) , ladder operator , shift operator , angular momentum operator , real representation , algebra over a field , hermitian matrix , pure mathematics , finite rank operator , eigenvalues and eigenvectors , quasinormal operator , compact operator , quantum mechanics , physics , angular momentum , total angular momentum quantum number , computer science , irreducible representation , angular momentum coupling , repressor , banach space , law , chemistry , biochemistry , political science , transcription factor , programming language , politics , messenger rna , extension (predicate logic) , gene
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.