A generalized deformed oscillator, with eigenvalues equal to the eigenvalues of the Schrodinger equation with the modified Poschl-Teller potential, is constructed. For special values of the potential depth the deformed oscillator algebra has a finite-dimensional irreducible representation. The polynomial representation and the associate deformed operations of integration and differentiation are studied. The results of this study are general and they can be applied directly to the case of the q-deformed oscillator, with q being a root of unity.
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C. Daskaloyannis (1992) studied this question.
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