The Classical Limit of Quantum Mechanics in a Curved Space Background

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David Elworthy, Aubrey Truman, Keith Watling

We give the semi-classical expansion, with remainder to any order in ℏ, for the wave function of a nonrelativistic quantum particle in a classical external magnetic field on a curved space background. The basic assumption is of a ‘‘no caustics condition’’ on the underlying classical mechanics, at least up to the time in question. The gauge invariance of the result is emphasized together with a discussion of the geometric meaning of the classical mechanical quantities involved.

T. F. Kamalov

This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields background. We are finding to the imagined Feynman Path a classical model of test particles as geodesic trajectory in the curved space of Projected Hilbert space on Bloch's sphere.

Wagel Siegel

This paper presents a comprehensive perspective of the metric of quantum states with a focus on geometry in the background independent quantum mechanics. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kahler & & manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space when the limit h → 0, we obtain the metric of quantum states in the configuration space without imposing the limiting condition h → 0. Here Planck’s constant h is absorbed in the quantity like Bohr radii 1 ~ a0. While exploring the metric structures associated with Hydrogen like atom,

Dipankar Home, S. Sengupta