Lie algebras for systems with mixed spectra. I. The scattering Poeschl--Teller potential

Journal Article · Wed May 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526559· OSTI ID:6054836

Frank, A; Wolf, K B

Starting from an N-body quantum space, we consider the Lie-algebraic framework where the Poeschl--Teller Hamiltonian, - 1/2 partial/sup 2//sub chi/ +c sech/sup 2/ chi+s csch/sup 2/ chi, is the single sp(2,R) Casimir operator. The spectrum of this system is mixed: it contains a finite number of negative-energy bound states and a positive-energy continuum of free states; it is identified with the Clebsch--Gordan series of the D/sup +/ x D/sup -/ representation coupling. The wave functions are the sp(2,R) Clebsch--Gordan coefficients of that coupling in the parabolic basis. Using only Lie-algebraic techniques, we find the asymptotic behavior of these wave functions; for the special pure-trough potential (s = 0) we derive thus the transmission and reflection amplitudes of the scattering matrix.

• Research Organization: Centro de Estudios Nucleares, Universidad Nacional Autonoma de Mexico, 04510 Mexico, D. F. Mexico
• OSTI ID: 6054836
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:5; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
AMPLITUDES
ASYMPTOTIC SOLUTIONS
BOUND STATE
BOUNDARY-VALUE PROBLEMS
CLEBSCH-GORDAN COEFFICIENTS
COUPLING
EIGENSTATES
EIGENVALUES
ENERGY SPECTRA
FUNCTIONS
GROUP THEORY
HAMILTONIANS
LIE GROUPS
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICS
MATRICES
POTENTIALS
QUANTUM OPERATORS
S MATRIX
SCATTERING
SCATTERING AMPLITUDES
SERIES EXPANSION
SO GROUPS
SP GROUPS
SPECTRA
SYMMETRY GROUPS
WAVE FUNCTIONS