Qutaibeh D. Katatbeh, Ma'zoozeh E. Abu-Amra
Abstract:
In this paper we derive close form for the matrix elements for
, where
is a pure power-law 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], [8-16] for power-law 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. Abu-Amra Department of Mathematics and Statistics, Faculty of Science and Arts Jordan University of Science and Technology Irbid 22110, Jordan |
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