Resonant states in momentum representation

Journal Article · Thu Mar 01 00:00:00 EST 1984 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.29.722· OSTI ID:6999367

Hernandez, E; Mondragon, A

Gamow states in momentum representation are defined as solutions of a homogeneous Lippmann-Schwinger equation for purely outgoing particles. We study their properties when the potential, local or nonlocal, is such that the trace of the kernel of the Lippmann-Schwinger equation exists. It is found that, contrary to what happens in position representation, Gamow states in momentum representation are square integrable functions. A norm is defined and expressions for matrix elements of operators between arbitrary states and properly normalized resonant states are given, free of divergence difficulties. It is also shown that bound and resonant states form a biorthonormal set of functions with their adjoints and that a square integrable function may be expanded in terms of a set containing bound states, resonant states, and a continuum of scattering functions. Resonant states may be transformed from momentum to position representation modifying, in a suitable way, the usual rule.

• Research Organization: Instituto de Fisica, Universidad Nacional Autonoma de Mexico, 01000 Mexico, D.F., Mexico
• OSTI ID: 6999367
• Journal Information: Phys. Rev. C; (United States), Vol. 29:3
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
LIPPMANN-SCHWINGER EQUATION
GAMOW BARRIER
BOUND STATE
CLUSTER MODEL
EIGENSTATES
MATRIX ELEMENTS
QUANTUM MECHANICS
RESONANCE SCATTERING
SCHROEDINGER EQUATION
DIFFERENTIAL EQUATIONS
EQUATIONS
INELASTIC SCATTERING
INTEGRAL EQUATIONS
MATHEMATICAL MODELS
MECHANICS
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
SCATTERING
WAVE EQUATIONS
653003* - Nuclear Theory- Nuclear Reactions & Scattering