Abstract
We present a simple analytical method, based on the symmetry transformations of the point group , to derive the exact energy eigenvalues and eigenfunctions of the stationary Dirac equation for a spin-1/2 fermion confined in a quantum billiard of an equilateral triangular shape with impenetrable boundary. Adequate boundary conditions on the Dirac spinors are proposed to preserve the self-adjointness of the Dirac operator, and guarantee the impenetrability of the probability current through the hard walls of the triangular billiard. The non-relativistic limit of our results are calculated and found to be in full agreement with their corresponding counterparts in the Schrödinger wave mechanics.
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