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The Mathematical Structure of Arrangement Channel Quantum Mechanics
Journal of Mathematical Physics
  • James W. Evans, Iowa State University
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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.

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

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American Institute of Physics
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James W. Evans. "The Mathematical Structure of Arrangement Channel Quantum Mechanics" Journal of Mathematical Physics Vol. 22 Iss. 8 (1981) p. 1672 - 1686
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