Tomasz Stachowiak
Published 2010-02-19, updated 2011-01-04Version 2
One dimensional Dirac equation is analysed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.
Comments: 3 pages, updated bibliography
Journal: J.Math.Phys.52:012301,2011
Relativistic Spin-0 Feshbach-Villars Equations for Polynomial Potentials
Symmetry operators and separation of variables in the $(2+1)$-dimensional Dirac equation with external electromagnetic field
Periods of relativistic oscillators with even polynomial potentials
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