Accession Number:

AD0623743

Title:

OBSERVABLES AND DERIVABLES PART II: UNIQUENESS AND EXISTENCE PROPERTIES.

Descriptive Note:

Technical summary rept.,

Corporate Author:

MATHEMATICS RESEARCH CENTER UNIV OF WISCONSIN MADISON

Personal Author(s):

• Gudder,Stanley P.

Report Date:

1965-07-01

Pagination or Media Count:

20.0

Abstract:

Certain uniqueness and existence properties of bounded observables are discussed. The uniqueness problem considers the question if two bounded observables have the same expectations in every state, are the observables equal. We say that an observable z is the sum of two bounded observables x and y if the expectation of z is the sum of the expectations of x and y for every state. The existence problem poses the question does the sum of two bounded observables exist. Only partial answers to these questions have been found. It is shown that the uniqueness property holds for simultaneous observables and certain classes of non-simultaneous or complementary observables. The existence property holds for simultaneous observables and a counterexample is given which shows that this property does not hold in general. Logics in which the uniqueness and existence properties hold are considered. Author

Descriptors:

• (*FUNCTIONAL ANALYSIS
• QUANTUM THEORY)
• (*QUANTUM THEORY
• FUNCTIONAL ANALYSIS)
• PROBABILITY
• OPERATORS(MATHEMATICS)
• ALGEBRA
• MATHEMATICAL LOGIC

Subject Categories:

• Statistics and Probability
• Quantum Theory and Relativity

Distribution Statement:

APPROVED FOR PUBLIC RELEASE