  The noncommutativity induced by a Drinfel'd twist produces Bopp-shift like
transformations for deformed operators. In a single-particle setting the
Drinfel'd twist allows to recover the noncommutativity obtained from various
methods which are not based on Hopf algebras. In multi-particle sector, on the
other hand, the Drinfel'd twist implies novel features. In conventional
approaches to noncommutativity, deformed primitive operators are postulated to
act additively. A Drinfel'd twist implies non-additive effects which are
controlled by the coproduct. We illustrate these features for a class of
(abelian twist-deformed) 2D Hamiltonians. Suitable choices of the parameters
lead to the Hamiltonian of the noncommutative Quantum Hall Effect, the harmonic
oscillator, the quantization of the configuration space. The non-additive
effects in the multi-particle sector, leading to results departing from the
existing literature, are pointed out.
