A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations

In this review article we discuss different techniques to solve numerically the time-dependent Schr\"odinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations bet\-ween these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.

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