2010/05/20 by Nölle, Christoph
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1005.3786
The classical limit ℏ->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schrödinger equation. In this paper I elaborate on an idea of M. Reuter to represent wave functions by parallel sections of a flat vector bundle over phase space, using the connection of Fedosov's construction of deformation quantization. This generalizes the ordinary Schrödinger representation, and allows naturally for a description of quantum states in terms of a curve plus a wave function. Hamilton's equation arises in this context as a condition on the curve, ensuring the dynamics to split into a classical and a quantum part.