  We show that the infinite-dimensional representation of the recently
introduced Logistic algebra can be interpreted as a non-trivial generalization
of the Heisenberg or oscillator algebra. This allow us to construct a quantum
Hamiltonian having the energy spectrum given by the logistic map. We analyze
the Hamiltonian of a solid whose collective modes of vibration are described by
this generalized oscillator and compute the thermodynamic properties of the
model in the two-cycle and r=3.6785 chaotic region of the logistic map.
