On the Numerical Solution Of Schrodinger Equation

Khadija A. Ben Mussa; Amna M. Gresh; Nagah A. Elbhilil; Ali M. Awin

Khadija A. Ben Mussa Department of Mathematics, Faculty of Science, University of Tripoli , Tripoli, Libya
Amna M. Gresh Department of Mathematics, Faculty of Science, University of Tripoli, Tripoli, Libya
Nagah A. Elbhilil Department of Mathematics, Faculty of Science, University of Tripoli, Tripoli, Libya
Ali M. Awin Department of Mathematics, Faculty of Science, University of Tripoli, Tripoli, Libya

Keywords: Numerical , Solution , Schrodinger Equation , Potential Morphing Method.

Abstract

In the beginning, we start with reviewing basic concepts such as inner product and Hilbert spaces ; then we introduce Schrodinger Equation focusing on the solution of time–dependent and time–independent with a stress on the harmonic oscillator problem which will be the ingredient for our subject ; namely, the numerical solution of .

The numerical solution of is then tackledusing the so–called potential morphing method .Calculations were carried out for the ground state of the which represents the frame of reference to work with. The obtained results were compared with similar ones and found to be in very good agreement. Finally, a brief discussion related to possible future work is given ; moreover recent works on the subject are exposed to

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