Abstract
A critical study of some elementary aspects ofq-algebras is presented. The results are: (i) theq-algebras are related to para-Bose (para-Fermi) algebras only when both reduce to the usual Bose (Fermi) case, (ii) after performing a linear transformation of the operatorsA andA† that satisfy theq-algebra relation AA†, a generalized version of Penney's theorem (in the sense that the new operators satisfy noncanonical commutation and anticommutation relations) is obtained, (iii) the spectrum of one of the Hamiltonians of the system is obtained from the correspondence principle, and (iv) a whole family ofq-algebra Hamiltonians is exhibited. This family has the property that the noncanonical commutation relation is stable.
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