Anomalous singularities in the complex Kohn variational principle of quantum scattering theory

Journal Article · Fri Dec 15 04:00:00 EST 1989 · Physical Review (Section) A: General Physics; (USA)

DOI:https://doi.org/10.1103/PhysRevA.40.6879· OSTI ID:7162404

Lucchese, R R ^[1]

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1. Department of Chemistry, Texas A M University, College Station, Texas 77843 (US)

Variational principles for symmetric complex scattering matrices (e.g., the {ital S} matrix or the {ital T} matrix) based on the Kohn variational principle have been thought to be free from anomalous singularities. We demonstrate that singularities do exist for these variational principles by considering single and multichannel model problems based on exponential interaction potentials. The singularities are found by considering simultaneous variations in two nonlinear parameters in the variational calculation (e.g., the energy and the cutoff function for the irregular continuum functions). The singularities are found when the cutoff function for the irregular continuum functions extends over a range of the radial coordinate where the square-integrable basis set does not have sufficient flexibility. Effects of these singularities generally should not appear in applications of the complex Kohn method where a fixed variational basis set is considered and only the energy is varied.

• OSTI ID: 7162404
• Journal Information: Physical Review (Section) A: General Physics; (USA), Journal Name: Physical Review (Section) A: General Physics; (USA) Vol. 40:12; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATRICES
MECHANICS
MULTI-PARAMETER ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
S MATRIX
SCATTERING
SCHROEDINGER EQUATION
SINGULARITY
VARIATIONAL METHODS
WAVE EQUATIONS
WAVE FUNCTIONS