Radon Transform in Finite Dimensional Hilbert Space

M. Revzen

Published 2012-01-02, updated 2012-02-06Version 2

Novel analysis of ?nite dimensional Hilbert space is outlined. The approach bypasses general, inherent, di?culties present in handling angular variables in ?nite dimensional problems: The ?nite dimensional, d, Hilbert space operators are underpinned with ?nite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in ?nite dimensional quantum mechanics studies. Interrelation among the Hilbert space operators revealed via their (?nite) dual a?ne plane geometry (DAPG) underpinning are displayed and utilized in formulating the ?nite dimensional ubiquitous Radon transformation and its inverse illustrating phase space-like physics encoded in lines and points of the geometry. The ?nite geometry required for our study is outlined.