Density Matrix Theory for the BDS-Hamiltonian

In the present paper, we have extended the usual uncertainty relations, as well as the entropic uncertainty relations to the mixed states, particularly to the thermal states, using the density matrix formalism. As quantum model we have choosen the quantum mechanical ideal gas with the harmonic oscillator-like Hamiltonian H, introduced by Beckers, Debergh and Szafraniec, generically named BDS-Hamiltonian.