Journal of Theoretical and Computational Studies
http://situs.jurnal.lipi.go.id/jtcs/
TOWARD THE PROPOSITIONAL CALCULUS OF UNSHARP QUANTUM MECHANICS
M.F. Rosyid, D.S. Palupi and W.S.B. Dwandaru
Work Group on Mathematical Physics, Department of Physics, Gadjah Mada University SEKIP unit III, 55281 Jogyakarta, Indonesia
Abstract
An assertion (see Theorem 1.1) dual to that of Naimark`` is argued. The assertion allows us to regard the unsharp`` quantum mechanics as a result of reducing the usual quantum mechanics by`` means of a kind of projection.`` An algebraical system P_{(H, \pi)} consisting of`` the projections lattice (P(H),\leq) of`` a Hilbert space H and an orthogonal projection \pi `` onto a closed subspace \tilde{H} of H `` is proposed as the mathematical interpretation or model of`` propositional calculus of the unsharp quantum mechanics.`` The mathematical structures surrounding H_{(H,\pi)}) `` are investigated.
