EIGENFUNCTION EXPАNSIONS FOR THE SCHRODINGER OPERATOR WITH A SQUARE POTENTIAL

Authors

  • A.Kh. Khanmamedov
    • D.H. Orujov

      Keywords:

      harmonic oscillator, Schrödinger operator, spectrum, eigenfunction, Weber function

      Abstract

      The Schrödinger operator L=-(d2/dx2)+θ(x)x2  is considered on the entire axis, where θ(x) is Heaviside function. The direct scattering problem for the operator L is studied. The formula is obtained for the expansion in terms of eigenfunctions of the continuous spectrum of the operator L.

       

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      Published

      2025-04-04

      Issue

      Vol. 78 No. 1-2 (2022)

      Section

      Articles