Symplectic integrators for the multichannel Schroedinger equation

Journal Article · Thu Jun 15 04:00:00 EDT 1995 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.468871· OSTI ID:64910

Manolopoulos, D E ^[1]; Gray, S K ^[2]

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1. Department of Chemistry, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
2. Theoretical Chemistry Group, Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)

The multichannel radial Schroedinger equation that arises in time-independent inelastic scattering theory and certain bound state problems has a classical Hamiltonian structure in which the radial coordinate plays the role of time. One consequence of this Hamiltonian structure is that the Schroedinger equation has symplectic symmetries, which lead in the context of inelastic scattering to the unitarity and symmetry of the {ital S} matrix. Another consequence is that so-called symplectic integrators can be used to solve the radial Schroedinger equation, both for bound state and scattering problems. This idea is used here to derive a new family of symplectic integrator-based log derivative methods for solving the multichannel radial Schroedinger equation. In addition to being simpler to write down and program, these methods are shown to be highly competitive with Johnson`s original log derivative method for several inelastic scattering and bound state test problems. An equivalent solution following version of the symplectic integrator family is also introduced and shown to have similar advantages over the DeVogelaere method. A number of more formal consequences of the classical Hamiltonian structure of the radial Schroedinger equation are also noted. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 64910
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 23 Vol. 102; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
BOUND STATE
INELASTIC SCATTERING
NUMERICAL SOLUTION
PHASE SPACE
S MATRIX
SCHROEDINGER EQUATION
SYMMETRY