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In this work we deal with Klauder’s approach, which is based on the construction of coherent states of the Heisenberg algebra.This algebra appears in many areas of modern theoretical physics and as an example we notice that the one-dimensional quantumoscillator algebra is an important tool in the second-quantization approach. The Hamiltonian of the physical system under someconsideration, in our context, belongs explicitly to the set of generators of the algebra, the other generators in this set being the stepoperators of the system. The version of the Generalized Heisenberg Algebra (GHA) is written using a general function called thecharacteristic function of the algebra, which is connected with the energy spectrum ofthe physical system under consideration. It wasshown that there is a class of quantum systems described by this GHA. This class is characterized by those quantum systems havingenergy eigenvalues written as successive energy levels and the characteristic function is a different function for each physical system.