1201.5143 (Tomasz Stachowiak)

On integrable rational potentials of the Dirac equation    [PDF]

Tomasz Stachowiak

The Dirac equation, when reducible to an ordinary second order linear
equation, exhibits a form of quasi-integrability, i.e. exact solutions exist
only for a particular subset of energies. The differential Galois theory can be
used to identify the integrable cases, recover integrable rational potentials,
explicit solutions and strictly rule out the remaining cases as non-integrable.
The effectiveness of this approach is demonstrated by providing a new class of
potentials for which the equation in question can be transformed to the
Whittaker form.

View original: http://arxiv.org/abs/1201.5143