Programs in Physics & Physical Chemistry
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|Manuscript Title: GAMOW: a program for calculating the resonant state solution of the radial Schrodinger equation in an arbitrary optical potential.|
|Authors: T. Vertse, K.F. Pal, Z. Balogh|
|Program title: GAMOW FUNCTIONS|
|Catalogue identifier: AAOD_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 27(1982)309|
|Programming language: Fortran.|
|Operating system: OS 28.F.|
|RAM: 94K words|
|Word size: 8|
|Keywords: Atomic physics, Normalized gamow, Scattering, Resonant states, Single particle solution, Schrodinger equation, Decaying states, Complex eigen-solution, Poles of scattering, Bound states in complex Potential, Other, General purpose, Differential equation.|
|Classification: 2.6, 4.3.|
Nature of problem:
The program calculates the normalized Gamow solution of the radial Schrodinger equation, i.e. the solution which is regular at the origin and has purely outgoing wave asymptotics, in a spherically symmetric complex potential of arbitrary form. Optionally either the complex energy eigenvalue in a given potential, i.e. the position of the pole of the scattering function S(E) or the strength of the short range potential belonging to a given energy value is computed.
Internal and external solutions satisfying the boundary conditions in the origin and the asympotic region, respectively, are generated by integrating the radial equation with the Fox-Goodwin method and from the mismatch of their logarithmic derivatives a correction to the eigen energy/potential strength is determined. The procedure is repeated with the corrected value till convergence. The wave function is normalized in the Zel'dovich sense by integrating numerically along a contour in the complex r-plane.
The present method does not work in the vicinity of zero energy and for unphysical resonances and antibound states.
0.5-3 s per iteration.
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