The Mathematical Structure of Arrangement Channel Quantum Mechanics

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1981-08-01
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Evans, James
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Ames National Laboratory

Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.

For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.

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Chemistry

The Department of Chemistry seeks to provide students with a foundation in the fundamentals and application of chemical theories and processes of the lab. Thus prepared they me pursue careers as teachers, industry supervisors, or research chemists in a variety of domains (governmental, academic, etc).

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The Department of Chemistry was founded in 1880.

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1880-present

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A non-Hermitian matrix Hamiltonian H appears in the wavefunction form of a variety of many-body scattering theories. This operator acts on an arrangement channel Banach or Hilbert space 1(;' = Ell ncr where ,r is the N-particle Hilbert space and a are certain arrangement channels. Various aspects of the spectral and semigroup theory for H are considered. The normalizable and weak (wavelike) eigenvectors ofH are naturally characterized as either physical or spurious. Typically H is scalar spectral and "equivalent" to H on an H-invariant subspace of physical solutions. If the eigenvectors form a basis, by constructing a suitable biorthogonal system, we show that H is scalar spectral on 'C. Other concepts including the channel space observables, trace class and trace, density matrix and Moller operators are developed. The sense in which the theory provides a "representation" of N-particle quantum mechanics and its equivalence to the usual Hilbert space theory is clarified.

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This is an article from Journal of Mathematical Physics 22 (1981): 1672, doi: 10.1063/1.525112. Posted with permission.

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Thu Jan 01 00:00:00 UTC 1981
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