On the Stability of Finite Difference Scheme for the Schrödinger Equation Including Momentum Operator

In this paper, we apply the finite difference method to a Schrödinger equation which contains a momentum operator. For this, we constitute a difference scheme. A priori estimate for the solution of difference scheme is obtained. By using this estimate, we prove that the difference scheme is unconditionally stable.

Keywords:

Schrödinger equation finite difference method, stability,

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