Observables, maximal symmetric operators, POV measures and their applications in quantum mechanics
Abstract
Approximate observables, their description in terms of POV measures and
the subsequent extension of the orthodox notion of observable are examined.
The sense in which the approximate observables are non-ideal observables
is considered and a generalised concept of ideal observable is proposed. The
conventional requirement of self-adjointness is relaxed to one of maximal
symmetry and the PV measures are replaced by the larger set of generalised
spectral measures of maximal symmetric operators. The implications for
the quantisation problem are discussed and we give some new examples of
observables which have no orthodox representation, i.e. observables which
can be identified with non-self-adjoint maximal symmetric operators. Particular
attention is paid to those aspects of the orthodox theory which rely
on specific properties of self-adjoint operators, such as their association with
the infinitesimal generators of groups of unitary operators, and we look at
the analogous properties in our generalised theory.
Type
Thesis, PhD Doctor of Philosophy
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