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We consider initial-boundary value problems for a generalized time-dependent Schrodinger equation in 1D on the semi-axis and in 2D on a semi-bounded strip. For Crank-Nicolson flnite-difierence schemes, we suggest an alternative coupling to approximate transparent boundary conditions and present a condition ensuring unconditional stability. In the case of discrete trans- parent boundary conditions, we revisit the statement and the proof of stability together with the derivation of the conditions.

On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. Part II