2018/06/14 by Tomas Zimmermann, Zimmermann, Tomas
Physics and Astronomy · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Quantum Physics (quant-ph) #physics.chem-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.1806.05383
arxiv created 2018/06/14 · arxiv updated 2018/06/15
A formulation of quantum mechanics is introduced based on a 2D-dimensional phase-space wave function \text\reflectboxp\mkern-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 Schrödinger 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 ei(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.