By Hilbrand Johannes Groenewold (auth.)
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According to the quantum notion of observation Oq the observer can in principle actually infer that conclusion under ideal conditions and he cannot infer more under any condition. This rule establishes the connection between the mathematical formalism and the observers perceptions. The rule does not follow from the formalism. The formalism is in harmony with the rule. The rule justifies the representation of the formalism in terms of pure quantum states. 30) of the extended or original object system is realized after this measurement.
14) (t 0 ,t1). This means that during this time interval the H a m i 1t o n i an H 12 (t) of the combined systems 1 and 2 cannot be split up into the sum of two H a m i 1 t o n i an s H 1(t) and H 2 (t) of the separate systems. The system 2 is supposed tobe initially in the pure quantum state cp20 (t0). We impose two conditions on H 12(t) and cp20 (t 0 ). 15) G~ is an operator with respect to the variables of 2 (q-number), but an ordinary number with respect to the variables of 1 (c-number). 16) given by .
01 Deviation. 01} Ex(k; a) = Tr(ka). 02) First we review some consequences of this definition, detached of any interpretation. 02) that the deviation is non-negative. We form the transition operators kvp. "p. v with Xvp. = Tr(kv,. k). p. = p. 04) 1. ,. ,. ,. ,. ,. ,. 05) can only be zero, if rp is a linear combination of eigenfunctions rp,. all with the same eigenvalue a,.. 07) Dev(k; a) = ~ k, Tr(k,a2) - (~ k,Tr(k,a)) 2 r = ~k,= ~ k,Dev(k,; r a) r + -! ; a))2. 08) ~ The deviation of a in the state k is therefore only zero, if all occuring states k, (k, > 0) in the mixture give zero deviation and the same expectation value for a.