Abstract
A formulation of quantum mechanics is introduced based on a 2D-dimensional phase-space wave function p-3mup(q,p) which might be computed from the position-space wave function ψ(q) with a transformation related to the Gabor transformation. The equation of motion for conservative systems can be written in the form of the Schr\"{o}dinger equation with a 4D-dimensional Hamiltonian with classical terms on the diagonal and complex off-diagonal couplings. The Hamiltonian does not contain any differential operators and the quantization is achieved by replacing q and p with 2D-dimensional counterparts (q+q')/2 and (p+p')/2 and by using a complex-valued factor e^i(q· p'-q'· p)/2 in phase-space integrals. Despite the fact that the formulation increases the dimensionality, it might provide a way towards exact multi-dimensional computations as it may be evaluated directly with Monte-Carlo algorithms.