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Modern Physics Letters A

THE EIGENVECTORS OF q-DEFORMED CREATION OPERATOR $a_q^+$ AND THEIR PROPERTIES

Guo-xin Ju, Jin-He Tao, Zixin Liu, MIAN WANG

Published Mar 14, 1995• 0 citations
Publisher

Abstract

The eigenvectors of q-deformed creation operator [Formula: see text] are discussed for q being real or a root of unity by using the contour integral representation of δ function. The properties for the eigenvectors are also discussed. In the case of qp = 1, the eigenvectors may be normalizable.
DOI
10.1142/s0217732395000715

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THE EIGENVECTORS OF q-DEFORMED CREATION OPERATOR aq+a_q^+aq+​ AND THEIR PROPERTIES
We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.
Eigenstates of the parabose and parafermi creation operators are constructed. In the Dirac contour representation, the parabose eigenstates correspond to the dual vectors of the parabose coherent states. In order p=2p=2p=2, conserved-charge parabose creation operator eigenstates are also constructed. The contour forms of the associated resolutions of unity are obtained.