Mathematical structure of arrangement channel quantum mechanics

Journal Article · Sat Aug 01 00:00:00 EDT 1981 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525112· OSTI ID:6245765

Evans, J W

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 C = direct-sum/sub ..cap alpha../H where H is the N-particle Hilbert space and ..cap alpha.. are certain arrangement channels. Various aspects of the spectral and semigroup theory for H are considered. The normalizable and weak (wavelike) eigenvectors of H 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 Moeller 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.

• Research Organization: Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 6245765
• Journal Information: J. Math. Phys. (N.Y.); (United States), Vol. 22:8
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM MECHANICS
MANY-BODY PROBLEM
DENSITY MATRIX
EIGENVECTORS
HAMILTONIANS
HILBERT SPACE
KERNELS
S MATRIX
WAVE FUNCTIONS
BANACH SPACE
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRICES
MECHANICS
QUANTUM OPERATORS
SPACE
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics