Vol. 59, No. 1, 1975

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A theorem on simultaneous observability

Tom Louton

Vol. 59 (1975), No. 1, 147–159

It is well known in abstract quantum mechanics, that when two observables have a joint distribution, a state can be found, in which both observables have a small variance. In order to consider a converse of this, a relation between two observables is defined. Say x and y are two observables and that when α is a state such that the variance of x in α is small implies the variance of y in α will be small. From the above relation it follows that there is a continuous function f, such that f maps the spectrum of x onto the spectrum of y. Further, y = f(x).

Mathematical Subject Classification
Primary: 81.62
Received: 11 June 1974
Revised: 25 October 1974
Published: 1 July 1975
Tom Louton