TY  - JOUR
ID  - Rybalko2018
LB  - Rybalko2018
AU  - Rybalko, Yan
TI  - Initial value problem for the time-dependent linear Schrödinger equation with a point singular potential by the unified transform method
ST  - Initial value problem for the time-dependent linear Schrödinger equation with a point singular potential by the unified transform method
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 6
SP  - 883
EP  - 898
DO  - https://doi.org/10.7494/OpMath.2018.38.6.883
UR  - https://doi.org/10.7494/OpMath.2018.38.6.883
AB  - We study an initial value problem for the one-dimensional non-stationary linear Schrödinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems on two half-lines, to which we apply the unified approach to IBV problems for linear and integrable nonlinear equations, also known as the Fokas unified transform method. Following the ideas of this method, we obtain the integral representation of the solution of the initial value problem.
KW  - the Fokas unified transform method
KW  - Schrödinger equation
KW  - interface problems
SN  - 1232-9274
ER  -