Eigenfunction expansion associated with the one-dimensional Schrödinger equation on semi-infinite time scale intervals (Q540804)

The paper presents an expansion theorem for the Sturm-Liouville problem on semi unbounded time scale intervals: \[ -[p(t)y^{\Delta}(t)]^{\nabla}+q(t)y(t)=\lambda y(t),~~t\in(0,\infty)_{\mathbb T}, \] \[ y(a)-hy^{[\Delta]}(a)=0,~y(b)+Hy^{[\nabla]}=0 \] where \(\Delta\) is the time scale derivative, \(\nabla\) is the backward time scale derivative and \([\nabla]=p(t)y^{\Delta}(t),\) \(\lambda\) is the spectral parameter.