Investigation of the Hylleraas Method for Determining the Potential-Energy Function from the Phase Shift
- 1 December 1969
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 51 (11) , 5112-5117
- https://doi.org/10.1063/1.1671909
Abstract
The Hylleraas solution of the quantum mechanical inverse problem of scattering theory is discussed. A practical method for deducing the potential from the phase shift by this method and a variant upon it is described. A simple example (a model potential function) is used to illustrate the procedure. For this case, first‐order results are obtained analytically, higher‐order results by (extensive) numerical computations. The method converges properly if there are no bound states. However, for the model problem under investigation, the procedure converges to yield a phase‐equivalent potential when the potential well contains a bound state.Keywords
This publication has 17 references indexed in Scilit:
- Inversion of Velocity-Averaged Differential-Cross-Section Data to an Intermolecular PotentialThe Journal of Chemical Physics, 1967
- Deduction of potentials from scattering phase shifts: (I). Neutral particlesNuclear Physics, 1966
- Interatomares Potential aus Streuexperimenten: K-HgThe European Physical Journal A, 1966
- Der Regenbogeneffekt und Interferenzerscheinungen bei molekularen St enThe European Physical Journal A, 1965
- Determination of a perturbing potential from its scattering phase shift and bound states energy levelsNuclear Physics, 1964
- On the inversion of eigenvalue problemsAnnals of Physics, 1963
- The relation between zero-energy scattering phase-shifts, the Pauli exclusion principle and the number of composite bound statesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1955
- A remark on the uniqueness of the potential determined from the asymptotic phaseIl Nuovo Cimento (1869-1876), 1952
- On the Connection between Phase Shifts and Scattering PotentialReviews of Modern Physics, 1949
- Remarks on the Determination of a Central Field of Force from the Elastic Scattering Phase ShiftsPhysical Review B, 1949