SYMPLECTIC INTEGRATORS FOR THE MULTICHANNEL SCHRODINGER-EQUATION
The multichannel radial Schrödinger 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 Schrödinger...
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| Формат: | Journal article |
| Опубликовано: |
1995
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| Итог: | The multichannel radial Schrödinger 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 Schrödinger equation has symplectic symmetries, which lead in the context of inelastic scattering to the unitarity and symmetry of the S matrix. Another consequence is that so-called symplectic integrators can be used to solve the radial Schrödinger 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 Schrödinger 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 Schrödinger equation are also noted. © 1995 American Institute of Physics. |
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