Solution of the 1d Schrödinger Equation for a Symmetric Well

@article{Carvalho2019SolutionOT,
  title={Solution of the 1d Schr{\"o}dinger Equation for a Symmetric Well},
  author={Lindomar Bomfim de Carvalho and Wytler Cordeiro dos Santos and Eberth de Almeida Correa},
  journal={Revista Brasileira de Ensino de F{\'i}sica},
  year={2019}
}
We suggest a mathematical potential well with spherical symmetry and apply to the 1d Schrödinger equation. We use some well known techniques as Stationary Perturbation Theory and WKB to gain insight about the solutions and compare them each other. Finally, we solve the 1d Schrödinger equation using a numerical approach with the so-called Numerov technique for comparison. This can be a good exercise for undergrad students to grasp the above cited techniques in a quantum mechanics course. 

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