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• W2084064983 abstract "The aim of this paper is to study the position and momentum operators in q-deformed oscillator algebras. The natural form of the position operator is Xp=qpN(a++a)qpN, where p is a real number. This operator is an operator representable by a Jacobi matrix. Using the theory of Jacobi matrices, the theory of classical moment problem and the theory of basic hypergeometric functions, it is shown that, depending on values of q and p, Xp can be unbounded symmetric operator [which has the deficiency indices (1,1) and, hence, is not self-adjoint, but has self-adjoint extensions], bounded self-adjoint operator with continuous simple spectrum or self-adjoint operator of trace class (therefore, with discrete spectrum with zero as the point of accumulation of eigenvalues). The connection of the q-deformed Heisenberg relation PX−qXP=1 for the position and momentum operators with a q-deformation of the quantum harmonic oscillator is also considered." @default.
• W2084064983 created "2016-06-24" @default.
• W2084064983 creator A5032081860 @default.
• W2084064983 creator A5041924275 @default.
• W2084064983 date "1996-02-01" @default.
• W2084064983 modified "2023-10-18" @default.
• W2084064983 title "On position and momentum operators in the q-oscillator algebra" @default.
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• W2084064983 doi "https://doi.org/10.1063/1.531419" @default.
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