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A generalization of the description of a quantum system in the time interval between two measurements is presented. A new concept of a generalized state is introduced. Generalized states yield a complete description of a quantum system when information about the system is available both from the past and from the future. The formalism of generalized states provides a natural language for describing many peculiar situations. In particular, situations in which one can ascertain the result of a measurement of any one of several non-commuting variables are analysed. 'Weak' measurements on quantum systems described by generalized states are discussed. The relation between 'weak' and 'strong' measurements is investigated.
Aharonov et al. (1991) studied this question.