On the transformation operator for the Schrödinger equation with an additional linear potential. (English. Russian original) Zbl 1447.81110
Funct. Anal. Appl. 54, No. 1, 73-76 (2020); translation from Funkts. Anal. Prilozh. 54, No. 1, 93-96 (2020).
Summary: The paper considers the Schrödinger equation with an additional linear potential on the entire real line. A transformation operator with a condition at \(- \infty\) is constructed. The Gelfand-Levitan integral equation is obtained on the half-line \((- \infty, x)\).
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 81U40 | Inverse scattering problems in quantum theory |
| 34A55 | Inverse problems involving ordinary differential equations |
| 45A05 | Linear integral equations |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
Keywords:
Schrödinger equation; additional linear potential; Airy function; transformation operator; inverse problemReferences:
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