Chemistry, Ames Laboratory
Journal or Book Title
Journal of Mathematical Physics
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.
American Institute of Physics
Evans, James W., "The Mathematical Structure of Arrangement Channel Quantum Mechanics" (1981). Chemistry Publications. 955.