A Review and Application of the Finite-Difference Time-Domain Algorithm Applied to the Schrodinger Equation
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A Review and Application of the Finite-Difference Time-Domain Algorithm Applied to the Schrodinger EquationAbstract
This paper contains a review of the FDTD algorithm as applied to the time-dependent Schrodinger equation, and the basic update equations are derived in their standard form. A simple absorbing boundary condition is formulated and shown to be effective with narrowband wave functions. The stability criterion is derived from a simple, novel perspective and found to give better efficiency than earlier attempts. Finally, the idea of probability current is introduced for the first time and shown how it can be used to radiate new probability into a simulation domain. This removes the need to define an initial-valued wave function, and the concept is demonstrated by measuring the transmission coefficient through a potential barrier.
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