| Popis: |
Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by four operators a, a †, N and the unity 1 such as [a, N] = a, [a †, N] = −a †, a † a = ψ(N) and aa † = ψ(N + 1). We discuss the conditions of existence of a scalar product expressed with a true integral on the space spanned by the e igenstates of a (or a †). We give various examples, in particular we consider functions ψ that are linear combinations of q N, q −N and unity and that correspond to q-oscillators with Fock-representations or with non-Fock-representations. |
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