Double stochastic matrices in quantum mechanics

Journal Article · Fri Aug 01 04:00:00 EDT 1997 · Foundations of Physics

DOI:https://doi.org/10.1007/BF02551435· OSTI ID:669885

Louck, J D ^[1]

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1. Los Alamos National Lab., NM (United States). Theoretical Div.

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande`s discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff`s theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n{prime}-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices.

• Sponsoring Organization: USDOE, Washington, DC (United States)
• OSTI ID: 669885
• Journal Information: Foundations of Physics, Journal Name: Foundations of Physics Journal Issue: 8 Vol. 27; ISSN FNDPA4; ISSN 0015-9018
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
MATRICES
QUANTUM MECHANICS
STOCHASTIC PROCESSES
SYMMETRY GROUPS
UNITARY SYMMETRY