1201.0465 (M. Revzen)

Radon Transform in Finite Dimensional Hilbert Space    [PDF]

M. Revzen

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.

View original: http://arxiv.org/abs/1201.0465