Quantum mechanics in configuration space in context

Abstract:To enhance the way in which wave-particle duality is implemented in the modelling of quantum mechanical systems, Bukhari et al. [New J. Phys. 27, 084501 (2025)] recently introduced an alternative approach to quantum mechanics, namely quantum mechanics in configuration space. This formalism is based on a physically motivated quantisation of Newtonian mechanics and promotes the classical position-velocity states (x,v) to pairwise distinguishable quantum states. The resulting |x,v> states form the basis of the Hilbert space of individual quantum mechanical particles and evolve along classical trajectories. In this paper, we consider the modelling of a mechanical particle in free space and put quantum mechanics in configuration space into context. It is shown that this formalism increases the continuity between quantum and classical mechanics by avoiding a conceptual inconsistency associated with the definition of momentum in canonical quantisation. In addition, we emphasise that standard quantum mechanics and quantum mechanics in configuration space are based on two distinct formulations of classical mechanics.

arXiv:2606.17622 [quant-ph]

(or arXiv:2606.17622v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.17622 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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