Geometry and Quantum Mechanics

Abstract

Attempts for a geometrical interpretation of Quantum Theory were made, notably the deBroglie-Bohm formulation. This was further refined by Santamato who invoked Weyl's geometry. However these attempts left a number of unanswered questions. In the present paper we return to these two formulations, in the context of recent studies invoking fuzzy spacetime and noncommutative geometry. We argue that it is now possible to explain the earlier shortcomings. At the same time we get an insight into the geometric origin of the deBroglie wavelength itself as also the Wilson-Sommerfeld Quantization rule.