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Manuscript Title: One-dimensional Schrodinger equation in the harmonic oscillator basis with various potentials.
Authors: S.-T. Lai, P. Palting, Y.-N. Chiu
Program title: HOTPOT
Catalogue identifier: ACVF_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 82(1994)221
Programming language: Fortran.
Computer: PC-486.
Operating system: DOS VERSION 5.0.
RAM: 1000K words
Word size: 16
Keywords: General purpose, Differential equations, Nuclear, Atomic, Molecular, Solid-state, Angular momentum, Wigner 3-j symbol, Harmonic oscillator Tensor.
Classification: 4.3.

Nature of problem:
The program calculates the one-dimensional Schrodinger equation with seven different types of potentials in the harmonic oscillator basis as formulated by Palting [1]. Those formulas are derived by use of the harmonic oscillator tensor method [2] which includes angular momentum coupling coefficients or Wigner 3-j symbols. It is of fundamental importance in the evaluation of matrix elements in atomic, molecular and solid-state physics, and also in molecular reaction dynamics and the calculation of the multiphoton ionization of radicals [3-6].

Solution method:
The program is based on the seven matrix element expressions [1] and includes one major function DW3J [7] and one subroutine in which the program [8] diagonalizes the energy matrix to find the eigenvalues and eigenfunctions. The basis size and the parameters can be varied according to the purposes of the user.

Running time:
The execution time required on the PC-486 to solve a one-dimensional Schrodinger equation with different potentials depends mainly on the basis size and the type of potential chosen. It can vary from several seconds to several minutes for a polynomial-type potential (depending upon the number of terms). For other kinds of potentials the computer time can be several minutes to several hours long, since the program uses double precision and, as the basis size increases, the terms of the summations also increase greatly. The maximum basis size is set to 80 and for polynomial potentials 15 terms are included. Both of these can be easily modified by users.

References:
[1] P. Palting, Int. J. Quantum Chem. 46, 257-270 (1993).
[2] P. Palting, Int. J. Quantum Chem., 40, 457 (1991).
[3] L. Infeld and T.C. Hull, Rev. Mod. Phys. 23, 21 (1951).
[4] W. Duch, J. Phys. A, Math. Gen. 16, 4233 (1983).
[5] Jaan Laane, Applied Spectroscopy, 24, 73 (1970).
[6] R.D. Johnson III, B.P. Tsai and J.W. Hudgens, J. Chem. Phys. 91, 3340 (1989).
[7] S.T. Lai and Y.N. Chiu, Comp. Phys. Commun. 61, 350 (1990).
[8] D.G. Liu, J.G. Hui, Y.J. Yu and G.Y. Li, Fortran Algorithms Cumulative Sources, Vol. II, Chinese Defense Industry Press (1984).