PUBLISHED PAPERS #04.15
| Davud Orujov. Some Spectral Properties of the One-Dimensional Schrödinger Operator with Additional Potential |
|---|
| Abstract. One of the main study areas in quantum scattering theory is the one-dimensional Schrödinger operator. For the past two centuries a substantial number of mathematicians have made contribution to the study of this subject. The paper at hand considers a one-dimensional Schrödinger equation with additional potential on the entire axis. Additional potential is of the form θ(x)x2, where θ(x) is the Heaviside step function. It is well known that the solutions to such equation are expressed by Weber function. By matching the solutions at x=0, representations of special solutions to the equation are obtained. Expansion formulas for these special solutions are then given using methods of Titchmarsh. |
| Keywords: Schrödinger equation, Weber function, expansion formulas, reflection coefficient, scattering problem |
 Download PDF |
| DOI: https://doi.org/10.30546/MaCoSEP2025.1021 |