One-parameter Potential from Darboux Theorem

@inproceedings{GaraRavelo2008OneparameterPF,
  title={One-parameter Potential from Darboux Theorem},
  author={J Gar{\'c}ıa-Ravelo and J. J. Pe{\~n}a and Jorge Noe Morales and Shi-hai Dong},
  year={2008}
}
Abstract: We consider the stationary one-dimensional Schrödinger equation with potential u(x; i) = 2 ∑ j=−2 fj(i)x , where the coefficients fj(i) are functions of a discrete parameter i. We establish the most general form of the coefficients fj(i) and obtain the ladder operators for the solution of Schrödinger equation by a Darboux transform. Generally speaking, the Darboux transform is obtained through a so-called superpotential W (x), which is derived from a Riccati equation. We first propose… CONTINUE READING