Unstable quantum states and rigged Hilbert spaces
Rigged Hilbert space techniques are applied to the quantum mechanical treatment of unstable states in nonrelativistic scattering theory. A method is discussed which is based on representations of decay amplitudes in terms of expansions over complete sets of generalized eigenvectors of the interacting Hamiltonian, corresponding to complex eigenvalues. These expansions contain both a discrete and a continuum contribution. The former corresponds to eigenvalues located at the second sheet poles of the S matrix, and yields the exponential terms in the survival amplitude. The latter arises from generalized eigenvectors associated to complex eigenvalues on background contours in the complex plane, and gives the corrections to the exponential law. 27 references.
- Research Organization:
- Texas Univ., Austin (USA). Dept. of Physics
- DOE Contract Number:
- EY-76-S-05-3992
- OSTI ID:
- 6228219
- Report Number(s):
- ORO-3992-351; CONF-781088-1; TRN: 79-012684
- Resource Relation:
- Journal Volume: 94; Conference: 7. international colloquium on group theoretical methods in physics, Austin, TX, USA, 14 Sep 1978
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HILBERT SPACE
QUANTUM MECHANICS
ENERGY LEVELS
SCATTERING
CORRECTIONS
DECAY AMPLITUDES
EIGENVALUES
EIGENVECTORS
HAMILTONIANS
RESONANCE PARTICLES
S MATRIX
SERIES EXPANSION
AMPLITUDES
BANACH SPACE
ELEMENTARY PARTICLES
HADRONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRICES
MECHANICS
QUANTUM OPERATORS
SPACE
TRANSITION AMPLITUDES
645500* - High Energy Physics- Scattering Theory- (-1987)
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics