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Physics Journal of the Indonesian Physical Society
http://situs.jurnal.lipi.go.id/pjhfi/   -   http://pj.hfi.fisika.net

TOWARD THE PROPOSITIONAL CALCULUS OF UNSHARP QUANTUM MECHANICS

M.F. Rosyid, D.S. Palupi and W.S.B. Dwandaru

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.