On integrable rational potentials of the Dirac equation

Details On integrable rational potentials of the Dirac equation On integrable rational potentials of the Dirac equation

2012-01-24

arxiv.org/abs/1201.5143v2

Physics

Mathematical Physics

5 pages. Ver2: updated bibliography

Scientific paper

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.

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