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Manuscript Title: Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions.
Authors: D. Lemoine
Program title: HODBT
Catalogue identifier: ADEX_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 99(1997)297
Programming language: Fortran.
Computer: Silicon Graphics R 4400.
Operating system: UNIX, UNICOS.
RAM: 6K words
Word size: 32
Keywords: Discrete Bessel transform, Cylindrical and spherical coordinates, Radial symmetry, Generalized finite basis and discrete variable representations, Nondirect product representations, Pseudospectral scheme.
Classification: 4.6, 4.7, 4.11.

Nature of problem:
In many applications it is appropriate to expand the sought function in terms of the bounded radial eigenfuctions of the Laplacian in cylindrical or spherical coordinates. These involve Bessel functions of the first kind, Jnu, with integer or half-integer order nu, and the computation of the integral Bessel (or Hankel) transform that generally has to be discretized.

Solution method:
In the case of bound state boundary conditions a full class of optimal discrete Bessel transforms (DBTs) is derived in a way similar to the discrete Fourier transform (DFT) in Cartesian coordinates. The grid points in both dual spaces are defined in terms of the zeros of Jnu when nu is conserved because of radial symmetry [1]. In the absence of symmetry a fixed-grid algorithm ensures an efficient DBT in nondirect product representations [2]. Despite their Gaussian- or DFT-like accuracy all those DBTs are nearly orthogonal but not quite [1,2]. Nevertheless, the overlap matrix procedure is straightforwardly applied to achieve orthogonality of the transformation with both grids unchanged [3].

Running time:
1 s (2 s) on a Cray 98 (Silicon Graphics R 4400 Indigo) for the test run.

[1] D. Lemoine, J. Chem. Phys. 101 (1994) 3936.
[2] D. Lemoine, Chem. Phys. Lett. 224 (1994) 483.
[3] G.C. Corey and R.J. Le Roy, J. Chem. Phys., submitted.