Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 64, pp. 115.
Matrix elements for sum of powerlaw potentials in
quantum mechanic using generalized hypergeometric functions
Qutaibeh D. Katatbeh, Ma'zoozeh E. AbuAmra
Abstract:
In this paper we derive close form for the matrix elements for
, where
is a pure powerlaw potential.
We use trial functions of the form
for
to obtain the matrix elements for
.
These formulas are then optimized with respect to variational
parameters
and
to obtain accurate upper
bounds for the given nonsolvable eigenvalue problem in quantum mechanics.
Moreover, we write the matrix elements in terms of the generalized
hypergeomtric functions. These results are generalization of those
found earlier in [2], [816] for powerlaw potentials.
Applications and comparisons with earlier work are presented.
Submitted February 19, 2008 Published April 28, 2008.
Math Subject Classifications: 34L15, 34L16, 81Q10, 35P15.
Key Words: Schrodinger equation; variational technique;
eigenvalues; upper bounds; analytical computations.
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Qutaibeh D. Katatbeh
Department of Mathematics and Statistics,
Faculty of Science and Arts
Jordan University of Science and Technology
Irbid 22110, Jordan
email: qutaibeh@yahoo.com 

Ma'zoozeh E. AbuAmra
Department of Mathematics and Statistics,
Faculty of Science and Arts
Jordan University of Science and Technology
Irbid 22110, Jordan 
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