Schrödinger equation with potential function vanishing exponentially fast

Abstract

Explicitly oscillating solutions of differential equation \[ y''+\left(\lambda+20\,{\rm sech}^{2}x\right)y=0\] and its eigenpairs are obtained by calculating complex residues. Eigenpairs, spectral function and eigenfunction expansions are also reported for this specific Pöschl–Teller differential equation.

Keywords

• schrödinger equation
• pöschl–teller potential
• complex residues
• explicit solution
• eigenpair