Quantum mechanics in the Gaussian wave-packet phase space representation

We present here some results related to an alternative mapping formulation (to the well-known Wigner-Weyl transform) which makes use of the Gaussian Wave Packet or coherent states representation |pq{left arrow, hooked}. The pair p-q which labels this state defines a phase-space in which the abstract operators P̂, Q̂, of momentum and position, are represented as differential operators. In the mapped expression of an operator A(P̂, Q̂), the quantum effects appear when they are absent in the corresponding Wigner-Weyl transform. © 1984.