  The Moyal and Voros formulations of non-commutative quantum field theory has
been a point of controversy in the recent past. Here we address this issue in
the context of non-commutative non-relativistic quantum mechanics. In
particular we show that the two formulations simply correspond to two different
representations associated with two different choices of basis on the quantum
Hilbert space. From a mathematical perspective the two formulations are
therefore completely equivalent, but we also argue that only the Voros
formulaton admits a consistent physical interpretation. These considerations
are elucidated by considering the free particle transition amplitude in the two
representations.
