We use the tridiagonal representation approach to solve the radial Schrödinger equation for the continuum scattering states of the Coulomb problem in a complete basis set of discrete Bessel functions. Consequently, we obtain a new representation of the confluent hypergeometric function as an infinite sum of Bessel functions, which is numerically very stable and more rapidly convergent than another well-known formula.

1.
A. D.
Alhaidari
and
H.
Bahlouli
, “
Tridiagonal representation approach in quantum mechanics
,”
Phys. Scr.
94
,
125206
(
2019
).
2.
A. D.
Alhaidari
, “
Solution of the nonrelativistic wave equation using the tridiagonal representation approach
,”
J. Math. Phys.
58
,
072104
(
2017
).
3.
A. D.
Alhaidari
, “
Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters
,”
Commun. Theor. Phys.
72
,
015104
(
2020
).
4.
W.
Magnus
,
F.
Oberhettinger
, and
R. P.
Soni
,
Formulas and Theorems for the Special Functions of Mathematical Physics
, 3rd ed. (
Springer
,
1966
).
5.
M.
Abramowitz
and
I. A.
Stegun
,
Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables
(
Dover
,
1964
).
6.
F. W. J.
Olver
,
D. W.
Lozier
,
R. F.
Boisvert
, and
C. W.
Clark
,
NIST Handbook of Mathematical Functions
, 1st ed. (
NIST
,
2010
).
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