• Corpus ID: 119008142

Quantum mechanical potentials exactly solvable in terms of higher hypergeometric functions. I: The third-order case

@article{Trachanas2011QuantumMP,
  title={Quantum mechanical potentials exactly solvable in terms of higher hypergeometric functions. I: The third-order case},
  author={Stephanos Trachanas},
  journal={arXiv: Mathematical Physics},
  year={2011}
}
We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of these potentials are explicitly computed and the peculiar properties of the discrete spectrum are depicted in a suitable phase diagram. Our starting point is a third-order formal eigenvalue equation of the hypergeometric type (with a suitable solution known) which is transformed to the Schr\"odinger equation… 

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