General deformed oscillators are studied. Unitary representations of the corresponding boson algebra are discussed. Many interesting properties of the spectra and matrix elements of the boson algebra are also presented.
This work addresses the study of the oscillator algebra, defined by four parameters p, q, α, and ν. The time-independent Schrödinger equation for the induced deformed harmonic oscillator is solved; explicit analytic expressions of the energy spectrum are given. Deformed states are built and discussed with respect to the criteria of coherent state construction. Various commutators involving annihilation and creation operators and their combinatorics are computed and analyzed. Finally, the correlation functions of matrix elements of main normal and antinormal forms, pertinent for quantum optics analysis, are computed.